*DAMN R6 Forum

Don't really know why that was locked...anyways

Bucc, I realize they were two seperate questions...hence my smilie...so I get full credit for the second part.

As for the first, you can't say that the only possible answer is Yes they do exist.  It can be proved either way.

UFO stands for Unidentified Flying Object
All Objects have an identity
To be unidentified an Object would have to have no identity
Therefore, no object can be unidentified.
Therefore, UFOs don't exist.

That it is flying is meaningless if you can disprove that unidentified objects exist.  And seeing as I've answered in the same number of statements than the "answer" I would get the full point for this part too.

Nope.  You wouldn't have.  Not only were the instructions specific, but when I read it, there was an assumption written after the smiley.  That's the way they were graded.


There are holes in that logic Bondo.

First, identity is subjective.  Your statement that "To be unidentified an Object would have to have no identity" is completely incorrect.  Since identification is up to the observer, and not to self, things can be unidentified.  When someone is annonomous, they are unidentified, when they tell you their name, they are identified.  Even if you say that something has to have an identity to itself, to have self, it would have to be self aware.  Since not all objects are self aware (unless you want to tackle that logical proof) they don't have their identity.  No matter how you slice it, anything can be unidentified, depending on your frame of reference.  

There is an important difference between IDENTITY and IDENTIFIED.  They do not mean the same thing.

Second, your first statement is suspect.  Do things that have yet to be discovered have an identity?  Do elements in science that we haven't given name or properties or behaviors have an identity?  How?  They exist, since we do find them and identify them.  But before being identified, don't they have to be "unidentified"?

Thrid, going back to your second statement, that is more of a premise to be proven, not a statement of fact.  

Fourth, you would be correct that flying wouldn't come into it, if the first parts of that argument were correct.

But you can approach it from multiple angles...one being a random person, one being from a universal view.  Lets say that the flying object was ice but the guy didn't know...whether he knows it or not, it is still ice...or more specifically H2O below 32?F.  Thus it identified from a universal standpoint...same goes for any object, so there are no unidentified objects.

Here is another one:
UFO stands for Unidentified Flying Objects
Flying is impossible due to gravity
Therefore no object can fly
Therefore UFOs do not exist.

Because scientifically, no objects can fly...all are falling due to gravity...they may have lift or propulsion, but they don't "fly".

I agree... No clue why it was locked... I'm going to answer it here. In the best way I know how: Laziness!

1) UFO's don't exist

2) I do not believe they do.

Ben

I think it was because Bucc said the answer to it?
Here's my version : 1) UFOs don't exist until I see one. 2) What you see is what you get.

There is the hole again.

You went from being unidentifed to a leap and identifing it.  Where did that leap come from?

If the guy doesn't know, to him it is unidentified.  Since that establishes that something CAN at sometime be UNIDENTIFIED, something can exist and be unidentified.

Again, you are trying to play word games, they don't work in logic.  Identity and Identify mean two different things.  Their meaning is important.


You are trying to get trickey with word games again Bondo, and that doesn't work.  Your statement that "flying is impossible due to gravity" is not a true statement.  You need to look up the definition of "fly" maybe.  

Word games don't belong in proofs.  Your argument is still flawed.  Flying is possible.  Things can go unidentified.  It's a sinking ship Bondo, get off now.

no Bondo, their is only one answer.  it would be, yes they exist.  untill, proved other wise.

time for questioning...

do we know all the possible objects? if not, then there remains some unidentified objects. say, if one person can't identify one object, there remains a unidentified object, to that person.
if, objects aquire a knowlege base of identities then would each item/person/thing retain these identities?

to say that, there are no UFOs, you would have to conluced, everyone knows everything.

does EVERYONE  know ALL the objects in space? after all, i'm sure we are discovering many new objects. aren't there gravitational pulls acting on everything, creating a active flight.

bah, although i didn't directly answer question 2. i don't like the answer. i don't think you need to say "why not".  I KNOW! maybe i need to get some sleep.  i'm questing everything... i need to stop.  i do feel like i can argue both ways now... but it would take research in scientific laws, the bottom line is you can only use laws.  theorys don't work.

Like I said, it depends on the angle you view it from...that is why it can be argued more than one way.  It can be logical that UFOs exist...or that they don't.  Like I've said before, logic is just the process, not a correct answer.

Bondo the idea of logic is questioning all sides, untill you come to a concluson.  Although, i don't see Bondo's logic.

it would be intresting to logicaly analyse if God exsists. then again, i don't see much logical proof that a mythical supreme being made the universe.

i do belive there was a philosopher that came to a logical conclusion that the universe was a miracle, in other words there has to of been a greater power to have been created.  But, from my knowlege he was a crazy guy.  he tried to create mathematical equations with his name and link it to jesus to prove that he was like some great guy or some crap.  anyways, i do remmber that he had great reasons to belive that there is a outsided force aka god.

Bucc, it is called Unidentfied b/c we know its a flying object, but exactly what kind of object, is unknown, wether its a balloon, space debris, or a piece of the us military

For those of you that want to read a logical proof on the existence on God, read Descartes' Meditations, specifically Meditations #1-6. Personally, I don't buy his reasoning, but it IS logical and my philosophy professor who is a noted epistemologist believes in it completely. Anyway, Descartes makes both ontological and cosmological arguments for the existence of god in those six meditations.

The logic behind if God exists pretty much get's caught up on two things.  On the pro side, faith can't be a fact.  On the con side, there is also no way to explain many things in the universe.  In other words, you can't really prove either side with existing knowledge.

Bondo, you just opened up that logic trap even wider.  You just said that it depends on how you look at it.  Guess what, it doesn't.  When you view it from every angle, there are cases when object are unidentified.  There was no stipulation that we are omniscient, and thus can identify everything.  That is exactly what I was getting at before.  Logic doesn't work when you used false statements as true.  You can't use a lie in logic.  Since we aren't omniscient, things do go unidentified.  Things also fly.  It's a simple argument that does have a very correct answer.  

The problem is that you are trying to change the conditions in order to make your answer fit.  Much the same thing you did in the gun ban debate.  In our universe, it is a fact that objects go unidentified.

so just out of curiosity, where did i lose points? i had the same basic idea as the answer, but i'd like to know were i went wrong

Religion as a whole is worthless to me. Look back thru out history and you will see that every major civilization had a religion simply because people have questions that can't be answered (like wtf am i doing hear, why do my feet stink, ect.). Old Religions, like the greek gods have the same relivance to modern christianity simply because all religion, or faith does is reasure us that there is a answer to our questions.
jesus is a whole other story. I'd  recon that he did indeed exsist. however the first record of his exsistance (gospel of mark) was written 66-70 years after he died. the only problem with this is that the writers of the gospels didn't even know him, leaving plenty of room for overexageration as the story of jesus was passed down after his death. If jesus was the true son of god i'd asume that most people would have acepted him, but no the Jews didn't belive him nor the romans. There is quite a bit of doubt surounding jesus' life and who he truely was.

essentialy no one knows what created us (with solid evidence), not me, not you. I"ll acept any religion anyone has, and i thinkt hat religion gives people something to do, and ways to help the community. I however am firmly against any form of christian influence in schools or in the government.

i'm getting tired of typing this, but maybe i'll type some more if someone challenges me (bucc  ;D )
and a little note about me, i was raised catholic, went to chuch almost every sunday, i've gone to catholic prep school for 15 years, and i never questioned god untill i was writing a term paper for a religioin class 2 years back.

bondo the question clearly ask "do ufo's exist?"

if you say that it CAN be logical that UFO's exist, then there you go, end your arguement there cuz you just answer it, they do. you wont get around it anyother way by saying "well it depends on the view",understand that if it works in one way, then it is true or in this case, exist.

thats like saying , for example, "do stinky feet exist?"

to some people they stink, to some people they dont. but if one person believes they stink, then stinky feet must exist.

i really hope what i said made sense, cuz i can be very unclear at sometimes.. or most times...

i just want to question the professors logic.

Question 1: Do UFO's really exist?
Proof:
UFO stands for Unidentified Flying Object
Objects exist
Objects can fly
Objects can be unidentified
Therefore: UFO's do exist

this can be trranslated to:
1.objects exist
2.some objects fly(not all fly)
3.some objects are not identified(not all are unidentified)
therefore,some objects fly, and some objects are not identified(doesn't mean there are objects both flying and unidentified at the same time).
this argument is true. the conclusion is false.
just becuase a object can take 2 actions, does not mean they can do both at the same time.  there is a differenace in "can", and "do".
1.objects can fly
2.objects can not fly

1.objects can unidentified
2.objects can be identified
showing that 2 actions can happen, doesn't imply they happen at the same time.

i see 3 possible answers.  i rest at you can not prove UFOs do or don't exist.

i hope this makes sence...

Although sometimes I wonder like who was before my mom and then before that person back to like animals and then trees and then leaves and then ya know whos farther back there has to be something but then again if there is anything out there never in our live times will we see it for I doubt theres anything in hte Milky Way and you wont be able to exit that by the time we die.

i'm sorry, i don't understand what you said, zait.  its to hard for me to follow through your post with one period; its hard to distinguish ideas if lacking the proper grammer.

zait, i recommend for you to learn grammer.  in college, i am learning what i missed in grade school, which is grammer. i was a slacker.

But what I'm saying is whether you consider nature or God your omnipotent being...there is one of them to which all objects are identified.  Thus there are no objects that are completely unidentified so as to be unidentified.  Just because one person doesn't know what they are doesn't make them truly unidentified, it just makes that person not omnipotent.  So seeing as every object is identifiable by this omnipotent being, there is no UFOs.  I'm not talking if there is UFO in the mind of humans but rather, is there a truly unidentified flying object.

Bondo,
I'll try this one more time.  You've said the answer yourself, but are just ignoring it.  Your argument about point of reference doesn't cut it for two reasons.

First, unless otherwise stated, you are talking about the human reference.  Since we are humans, we don't qualify our questions to ourselves, but we do qualify them to other things.  Also, for your point of view on God, you'd have to 1) prove that he exists and 2) prove that he's omnipotent.  Which are not facts to many here seem to agree with.  If Nature is your argument, you'd have to prove that nature is a thinking, reasoning being, because you are personafying nature that way.

Second, since there wasn't a distinct frame of reference (God, The Universe, Humans), they all have to be considered if that's your way of thinking.  If UFO's exist in any of those cases, then they exist.  So, even if something can't be unidentified to God, it can be to humans, therefore, it still can be unidentified.  There was nothing limiting this to just God, even in your arguments.  You narrowed the frame of reference to just fit your answer.  If you had widened it to include all frames of reference, then they still exist  (absolutes are so hard to prove, and that's what you were trying.)

Zaitsev, I still have no idea what in the world you are talking about.

Rob,

Very very good effort, but not quite right (in logic).
First, the joining of the sets was shortened.  But at that point the addition of one statement (fact) can change that.  All that would need to be added is "Objects that fly can be unidentified".  There was nothing excluding the two, so it didn't have to be added unless questioned (shortest possible again).

Second, can vs do.  Very good thinking, but there is a Theory/Law somewhere (I'd have to look it up) that says "If something can happen, then somewhere, sometime, it does happen".  There's also another way to look at this.  Can and Do are often used interchangably.  So, if you just substitue "some objects do" for "objects can", it gives you back the single conclusion.  

Proof:
Objects exist
Some objects do fly
Some objects are unidentified
Not all flying objects are identified
Therefore: UFO's really exist.

I added the fourth statement for you.  This answer isn't as short as possible, but that was because of your first question.

Now, If you want to prove that conclusion wrong, you have to prove the opposite, or challenge the statements.  And since I could easilly demonstrate an UFO, you would lose.  Imagine I take you to your backyard at night, and show you something that is all lit up and hovers over you before leaving.  Without my telling you, it would be unidentified.  You just have to get into the definition of unidentified is all.  You could argue that since I knew what it was, it was identified, then I'd just show you plenty of places where the Air Force listed things as UFO's, because they didn't know what they were.

bucc. you still didnt answer why i lost so many points on that little quiz. i'd like to know where i screwed up

Sorry Brain,

You argument for a ufo was basically logical, but it was too long and wandered (and you didn't change the meaning of what UFO stood for, even though you said you did).  You would have gotten the half point for comeing to the right conclusion in a more or less logical way.

You don't get any points for the second question, which was WHY?  You never answered that question.

i thought i had rolled that into the first answer. if they cant, not exist, then why isnt a valid question(or at least one that would be redundant due to the fact that in the process of proving that they must exist, you have already given the reason why)

oh well, i never was any good at tests anyway

Do you happen to have any more Bucc?  Post in a new thread if you do.  . .this one is turning into a theological debate

Brain, I'll take a wild guess and say that you didn't read my answers in the old thread.  Why? was a seperate question, not part of the UFO question at all.  Check the old thread really quick.

Loucnotes, I'm sure I can come up with a bunch if I think about them.  These only came up as part of a conversation I was having the other day.  I'll post a couple more for ya though.

Yeah, now that I have half a clue how the answer is supposed to be formatted, I should do better. Also, knowing that "Why not?" is an acceptable response helps. Was it just me or did anyone else think of that and not use it because it seemed so inherently 3 year old-ish?

Only about 99% of the people that see that question Ace.  It teaches an important lesson though.  Often the simplest answer is the right one.  

I am almost positive UFOs exist because of these reasons

1.) We live on a planet in a Solar system.

2.) We happen to be the same amount away from the sun, close enough not to freeze and close enough not to be to hot so we can have lifeforms.

3.) We live in a Galazy, how many of these?

4.) Our Galazy Is in one univers how many of those are there?

5.) There are TRILIONS AND TRILLIONS (if not more trilians) of universes.

6.) What do u think the chance is that one planet is the same distance away from the sun as earth??

7.)Than there is a pretty large persentage that there is life elcewhere than earth
_____________________________________________________________________________________

There may not be UFOs around earth but i know that they are real

-SK

That would have gotten 0 points Silent Killer.

Ok Bucc, I don't know if we are both ready to fully argue this, it can be rather time consuming in research.  I will agrue "we can not conclude UFOs do or do not exist, due to lack of hard complete factual data", while, you may argue "UFOs do exist".  Although, I haven't taken a logic class, yet.  I will try to the best of my ability.  And hey, we can enjoy learning from each other:).  First, I will question vary much, Seeing how we must question the arguments to get to the basis.  

To determine if each  statement  Is true, we must have a "law" to back it up.  While, a "theory" has not been fully proven.  For example, the "Theory of Evolution" is highly debateable, simply becuase it has not been proven.  While laws are mainly undisputed, due to intence proof and the consistancy.  Also, Einstein has showen Newtonian "Laws" of mechanics do not explain everything, Just because Newtonian mechanics is "wrong" in some situations, and so, it became a theory.  From what I know, there are vary few scientific laws, and many theories.  Theories tend to be more broad; laws, more specific, many times mathematicaly justifiable. More than likly, theories don't become laws; from how complex this world is.

So we can't say "If something can happen, then somewhere, sometime, it does happen" as you parifrased.  I'm almost positive(I am postive, but we must be open minded) there are some exceptions, therefore is a theory.  So, How would we know if in this case about UFOs would be an exception?

BTW, I may add, coming across this link to a university about this stuff, where I goten info.
http://science.kennesaw.edu/~rmatson/Biol%203380/3380theory.html

Rob, while your thinking and research do you credit, you seemed to miss that I could show you a ufo at any time.

But, on to the fun stuff of evaluating your logic.


Not so.  If I say it is snowing (because it is outside my window right now) we don't need a law to prove that.  Logic is often used to prove theories enough to make them laws.  

But, I can see what you are trying to get at, so let's move on.


Ok, I'm going to stop right there.  I was just writing about the rest of your argument when it struck me that, while not on any exam I took, it is a wonderful new logic question for the group.  I'll post it in a new topic.

As for the last one Rob, While you may not (and don't have to) accept the law (or theory, if you don't buy it) that "if anything can happen, it has at someplace and sometime", there were two other ways to prove that the arguments statements were true that I named (both by trial and by record).  Since it only has to happen one time and one time only to exist, I think I've made that point.

yea, i read the answers bucc, i jutd tried to roll it all into one little package.

Bucc, seeing how I personally wish to question all sides, I will play devil's advocate, as I've been, so there is questioning that should take place from all side.  While my very first argument has shown a side of my veiws, there is another that needs pure facts.

How about you point out a UFO, and I will try to deffend my argument.  This is a simple way to handle this(remmber if you point out one UFO then, my argument is shot).


Hehe, you sugesting we just belive you, that there is snow becuase you say you see it.  I can say you might be hallucinating(most likly not, hehe).  So you can't prove there is snow by your sight, your sight could even betray yourself.

Honstly, I belive you;logicly based on pure facts, no.



Perhaps, I should of said "For example, the "Theory of Evolution" is highly debateable, simply becuase it has not been proven enough to become a law, as it remains a theory"  probably would of been a better statement.


Please, bombard me with these trials and records.  As I have said above, pointing out instance of UFOs may be the best solution to be used to conclued.  And yes, it only takes one UFO to show existance of UFO(s)(logicaly enough :D).  But, my side will be hardest to defend, obviously.  foolish me for picking the hard side :(.

Actually, yes, obeservation still counts as a fact.  You can challenge that fact, just like any other.  If you had challenged it, I could then take a picture, or provide others that observed it.  Or, I could steer you to third party reports, like the local weather, that would verify that fact.  It is still a fact.  All you can do is challenge it if you don't believe it.  (Observations without conclusions are different from Opinions.  Opinions are not fact, they are conclusions.  That is a HUGE difference).


Nope.  It's not better and you'll see why in the other thread.  But let's give others the chance to chime in on it.


For evidence, I'll just include a link or two, of official government documents that had to be released in the name of the "Freedom of Information Act".  This first one (http://www.blackvault.com/documents/ufos/oasd/asod31.htm) shows a report of objects flying, changing direction and speed, shown both by radar and human observation.  Near the bottom you will notice the words "unidentified objects".  

This second tidbit (http://www.blackvault.com/documents/ufos/oasd/asod14.htm) is the executive summary (first page) of Project Blue Book.  You'll notice that they even define what a UFO is (very complete of them).  You can go on and read all the actual reports in there.  Notice they still have the category "unidentified" even after their investigations, meaning in some cases, they still didn't know what it was.

 (http://dynamic.gamespy.com/~damnr6/yabbse/YaBBImages/icon_bluh.gif)

Bucc's Logic test

1.  Yes
2.  I said so.

What I get?

 (http://dynamic.gamespy.com/~damnr6/yabbse/YaBBImages/beer.gif)

My logic question:

Five friends have access to a chat room.  Is it possible to determine who is chatting if the following info is known? Either Kevin or Heather, or both, are chatting.  Either Randy or Vijay, but not both. are chatting.  If Abby is chatting, so is Randy.  Vijay and Kevin are either both chatting or neither is.  If Heather is chatting then so are Abby and Kevin.  Explain Reasoning.

 :)

Ok, so we are at "right untill questioned wrong".  Niether of our sides has proved the other wrong, yet.  So are both sides right still? On a side note, is this how we must disprove a conclusion? with questions?

I do think I challenged your fact, but now I will clearly challenge it.  
What makes your fact true? And why?


I do think my startement was better, just didn't float your boat :).  I think I see your point though.  If I took "highly" out it would be a even better sentance.  But the theory of evolution has not become a law yet.  Why is that?  Perhaps some higher level thinkers are at confict with it, from spoted holes in the argument.  But we do know there is a reason why is not a law.

For the links:

From the start I can claim "there must of been a electronical malfunction, causing the radar system to not work properly".  can you give us the infomation to suport the radar wasn't lying or deceiving?

For the ground witness, do we have blood test at the time this was reported?  They ALL could of been taking drugs, causing these answers.

where are the facts that these people truly reported this and this is not just made up?

How do we know if the SAM sites were hearing the F-106s?
As for "lights in the sky".  There are stars, and other things that can reflect.  the witnesses could of been observing reflecting objects.  Therefore, they clam there were lights in the sky.

I belive the 2nd link just shows the air force is trying to investigate claimed UFOs.

Any other claimed UFOs? I prefer you would be the source of info, rather than a another internet site.  Becuase I will question to the point that the sites can't answer or reply the.

I think you missed my point.  A statement that "it is snowing outside my window right now" is a fact (I'm pointing out that facts are not the same as laws).  If you disagree with one of my facts (aka statements) you can challenge it.

There are a few ways to disprove a conclusion.  You can prove the opposite is true, you can point out a hole in the logic (which is one you were attempting before) or you can challenge the validity of the facts.  For example, in the gun thread, I was challenging both the validity of his facts and the soundness of his logic.

Again, another difference is an observation vs an opinion.  Opinions are formed from observations.  Opinions are conclusions.  Saying it's snowing is an observation.  Saying it's too early in the year for snow is an opinion.

I'm still going to leave the Evolution question for the other thread.  I want to give others a chance to talk about it before giving it away Rob.


In a courtroom, those questions may or may not fly.  In logic they don't.  

I probably didn't explain this well (like I said, I wouldn't make a good teacher).  Challenging a statement isn't just postulating how it could be wrong.  It's showing evidence to the contrary.  If you want to successfully challenge those facts in logic, you have to have something besides personal opinion on why they wouldn't be true.  You start by challenging a statement, which you did.  You asked for evidence, which was shown.  To challenge that, the burden is upon you to show evidence refuting what was shown (not an easy task, especially with a gimmie argument like this).


Actually, the source of the information was the documentation on Project Blue Book.  If you had gone on past the first page you would have seen actual studies and outcomes.  Some of which remain "unidentified" to the USAF.  The work was sited, and though the size of the document is large (you probably didn't leave the first scanned page, did you?) you can see on the 7th page (http://www.blackvault.com/documents/ufos/oasd/asod21.htm) that out of all the investigations that took place of UFO's, 701 are still classified as UFO.  If you are going to challenge a source, you should read the whole thing first.

It is impossible to determine for certain.

Say for example that Heather is chatting.  Abby must be, and therefore so should Randy.  Kevin must be as well.  Thus Vijay is chatting.  However, Vijay and kevin cannot both be chatting, so we know this is false.

Thus heather is not chatting.  This means that Kevin is chatting.  And thus Vijay is as well.  From this we can determine that Randy is not chatting.  However, there is not way to be certain as to whether Abby is chatting.  Randy is definitely chatting if she is, but he may be whether she is or not.  And simply because she definitely would chat in presence of Heather, doesn't mean she would not otherwise.

So to sum up, here is what can be determined:

Heather - not chatting
Kevin - chatting
Vijay - chatting
Randy - not chatting
Abby - Either

Rules:
Either K or H, or both, happening
Either R or V, but not both happen
If A is happening, so is R.?
V and K are either both happening or neither is
If H happens then so are A and K

You can replace happening with chating.


if K is picked then you can not have R
if A is picked you must have R then you can not use K if there is A or R
rule,If H happens then so does A and K
if A and K happen then R and V happen
rule, Either R or V, but not both
therefore,H can not happen
if H can not happen then we must pick K
rule,if K happens then V happens
rule, Either R or V, but not both happen
therefore, R can not happen
rule, if A happens then R happens
rule, Either R or V, but not both happen
therefore, V must happen

Conclusion, H, R, and A can not happen. There are only 2 rules saying you must pick 1 name, making 2 people must be picked.
Only K and V work.

let me know if how well this makes sense.

for Bucc's post, I will handle later.

if R not V
if V not R (doesn't need to be here)
if A then R
if V then K
if not V then not K
if H then A and K

Given R or V ; K and/or H (K, H, R, V, A)

First R
R
Not V
Not K
Not H
A is not resolvable (bad wording in the problem)

Conclusion: Can't be R because no K or H

Second V
V
Not R
Not A
K
Not H

Conslusion: Could be V and K, Fits all arguments

Third K
K
V
Not R
Not A
Not H

Conclusion: Could still be K and V.

Fourth H
H
A
K
V
Not R
R

Conclusion: invalid.

Fifth K and H
K
H
A
R
V
Not V

Conclusion: Invalid.

Final Conclusion: From that statement only V and K could be chatting together.  Vijay and Kevin.

If anyone wants to see the complete work, let me know.

Ah Bucc you're right.  I misread the statement about Abby and Randy.  Abby can't be chatting.  

Interesting how we got the same answer (well, I would have if I hadn't screwed that one statement) but with very different ways to go about it.

Doesn't surprise me at all Loudnotes.

I used shorthand, and just a very simple model to run the proof.  it works really well for math and computer programming too.

But that is by no means the only way to do it.  Logic is a disapline, as I've said, but it's also one that comes pretty naturally to, for lack of a better word, geeks.  Almost everyone here (there are some noted exceptions, and i'm not talking about bondo) has a basic understanding of logic.  How one thing leads to another.  People usually get tripped up because they don't know the major traps (or don't care).  Things like letting opinions in, or just linking two things that aren't.  But that's why there is debate.

Funny, whoever that new account was that posted it, deleted it too.  Maybe they will come back and let me know if that was an intentional typo in the problem, or if it was meant that way to make it easier to solve.