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a = b
a^2 = ab; multiplied by a
a^2 - b^2 = ab - b^2; subtracted b^2
(a-B) * (a+B) = b * (a-B); a^2 - b^2 is differance of two squares, factored b from right side
a + b = b; devided by (a-B)
a + a = a; substituted a for b
2a = a; combined the a's
2 =1; plugged in 1 for a
There are no errors in math on this page, only an error in logic.
What is the error in logic?
ahh, yes! I found the answer... hehe, I think.
(a-B) * (a+B) = b * (a-B); a^2 - b^2 is differance of two squares, factored b from right side
a + b = b; devided by (a-B)
since a=b, (a-B) = 0, which means if you devide both sides by (a-B), the result is undefined, and thus your argument is invalid.
Nice problem though, got me thinking for a couple of minutes. I love little problems like that, especially when I need a good reason to procrastinate my CS labs.
well dammit!!! I expected this one to be a stumper...oh well, how 'bout a weekly riddle or math...called The s00p Kitchen?
had you seen this one before? :wink:
s00p kitchen, sounds like fun. :)
No, I hadn't seen that one before. It actually puzzled me for a little bit. Had to look at every step about four times till I saw something wrong. It helped me knowing that there wasn't a mathematical error, hehe, otherwise it would have taken me longer I think.
I've taken an abstract math class here in college, which dealth with mathematical proofs. Neat stuff, like proving that 1 > 0.
Just a sidenote, there's proof that women are evil... hmm, let me see if I remember. Goes something like this:
a woman is like time and money, so therefore we have
woman = time * money
since time is money,
woman = money * money = (money)^2
now, as a separate equation, we have that money is the root of all evil, so we have:
money = square_root(evil)
if we square both sides, the square root cancels and we have:
(money)^2 = evil
plugging the value for (money)^2 in the second equation, we have:
woman = evil
So lets pray for all the evil female beings in this forum... :pope: hehe
sort of like motus totems (ponens, something, what?)
q = All roses
r = are flowers
q -> r
q
:. r
but not
q -> r
r
:. q
eh?
here's a congratulatory smily, I'll post the first s00p's kitchen in the lobby sometime next week.
:goodjob:
oh, and the philosophy behind it is that reason and logic trump math.
That's a cool riddle. I used something like it in my recent thread "2 + 2 = 5!!!". The point of that thread was to get people to argue the best they can for something they don't agree with. Somebody argued that you cannot divide by zero (arguing what they do believe, to keep my argument going), and I said that that is based on a false premise because the notion is based on the principle that there is nothing zero can be multiplied by to get another number. I said that if zero is muliplied by more than infinity, another number can be reached. I also showed that 0 = 1, and any number can be divided by 1. 0/0 is possible because 0 x 0 = 0. Also, any number divided by itself is 1. 0/0 = 1 because 0 x 1 = 0. Thus, 0/0 is a legitimate figure. It is both 0 and 1, so 0 = 1. Based on the same principle, 0 = any number. That equation is the formula for the origin of existence. There is no problem with dividing by 1, so there is no problem with dividing by 0.
0/0 = 0 (because 0 x 0 = 0)
0/0 = 1 (because 0 x 1 = 0)
1 = 0 (substitution property of equality)
The same holds true of all numbers, not just 1, so...
0 = everything
(Nothing exists.)
Nothing is not anything,
so it is not not anything.
Nothing is anything,
therefore it is everything.
0/0 graphically speaking, is indeterminate. There aren't any solutions that can be derived from it. However, let's say that a conclusion reached a philosophical 0/0. That conclusion can still be reworked.
I think it means that sharpe make me high. mmm...bisc.
nice match puzzle... back in the day in high school our 11th grade teacher showed us this one.
Universal, all you showed with your little spiel there is that you might be a raging lunatic ;)
Anyways, what does this recent burst of math riddles have to do with philosophy?
Well, my point about philosophy was that even though math appears to be the most concrete method we have of modeling our universe, logic and reason are essential to math, just as emotion is central to art.
Well, I would have to believe it for that to be the case. Since you chimed in, what is your counter analysis of my devil's advocate argument? You are always quick to make negative comments about other people's arguments, but I have yet to see an actual counter argument from you. Let's see one.Quote:
Originally posted by dream-scape
Universal, all you showed with your little spiel there is that you might be a raging lunatic ;)
And aren't you the person who said a bunch of stuff about real life gods coming into people's dreams and turning them into gurus? People who live in glass houses shouldn't throw stones. ;)
What this stuff has to do with philosophy is that it gets to the heart of the order of reality, which math represents. I'm not talking about just the symbols, but the realities the symbols are used to represent. We are talking about the philosophy of math, which involves the philosophy of the nature of reality. If 1 really does equal 2 or 0 or any other number other than itself, then we all need to start our philosophical thinking all over.
Read my sig, if you can :lol:Quote:
Originally posted by Universal Mind+--><div class='quotetop'>QUOTE(Universal Mind)</div>Actually all you have done up to this point is play math puzzles. Yes intellectually stimulating, but not philosophical.Quote:
We are talking about the philosophy of math, which involves the philosophy of the nature of reality.[/b]
<!--QuoteBegin-Universal Mind
And aren't you the person who said a bunch of stuff about real life gods coming into people's dreams and turning them into gurus? People who live in glass houses shouldn't throw stones. ;)
You entire silly sales pitch is based upon the idea that there can be a number greater than infinity, and that infinity can be used in computations.Quote:
Originally posted by Universal Mind
Well, I would have to believe it for that to be the case. Since you chimed in, what is your counter analysis of my devil's advocate argument? You are always quick to make negative comments about other people's arguments, but I have yet to see an actual counter argument from you. Let's see one.
However, as I'm sure you are aware infinity is a concept. It is not a real number. You can never reach it either. There is no such thing as a real number larger than infinity or smaller than negative infinity. If you think you have reached infinity, you're a bit off because #1 you're not there yet and #2 it is not a real number.
You also cannot use it in computations, being it is only a concept. 0 x infinity equals one crazy day.
And also as you divide by smaller and smaller numbers towards 0, the answer becomes larger and larger (1/.10; 1/.01; 1/.001; 1/.0001; etc). You can keep doing that forever without reaching 0 in the denominator, so 1/0 is undefined. It is not infinity, but we might say as the denominator approaches 0, the answer approaches infinity, but neither ever gets there.
You could also think of it in simpler terms as, how many units of 0 does it take to equal 1? The answer is what the hell kind of question is that? You can add as many units of 0 together as you like for as long as you live and you will never reach 1 or any other number other than 0.
A damn good one! Plus, infinity can take more than one space on the number line (meaning it's either a really special happy number, or just not one at all)...Quote:
You could also think of it in simpler terms as, how many units of 0 does it take to equal 1? The answer is what the hell kind of question is that?[/b]
-------------------0---1------------------------...----------(infinity)--------------(infinity)---(infinity)-------------------------------------------------------------------------------------(also infinity)
1 also = :? (a confused yellow person)
But math is a sort of philosophy...
N = N* fp ne fl fi fc fL
My "sig" would give you a cule.
N* = the number of stars in the Milky Way galaxy:
fp = fraction of stars with planets around them:
ne = number of planets per star ecologically able to sustain life:
fl = fraction of those planets where life actually evolves:
fi = the fraction of fl that evolves intelligent life:
fc = the fraction of fi that communicates:
fL = the fraction of the planet's life during which the communicating civilizations survives:
P.S. Sorry I couldn't help it, had to pose this one, It will blow your mind!
Sorry man, but that proof doesn't hold, and for the same reason that the other trick proof didn't hold. Your argument is convincing and almost makes sense.Quote:
Originally posted by Universal Mind
0/0 = 0 (because 0 x 0 = 0)
0/0 = 1 (because 0 x 1 = 0)
1 = 0 (substitution property of equality)
The same holds true of all numbers, not just 1, so...
0 = everything
(Nothing exists.)
Nothing is not anything,
so it is not not anything.
Nothing is anything,
therefore it is everything.
However, a number divided by 0 is undefined through mathematical axioms. Those are basic rules (few more than 10) which define the entire number system. Through those axioms, it is possible to prove that if X = A / 0, for any A belong to R (Real numbers), then the number X does not exist. Using a proof in which relies in the use of a number being divided by 0 nullifies that proof, and thus they're good only as a puzzle for people to figure out what is wrong with the proof. I can't remember the proof that shows that a number can't be divided by 0, but I'll get back to you if I ever get englightened and remember... hehe.
Saying
0/0 = 1 (because 0 x 1 = 0) is pretty much the same to saying
1 = -1 (because (1)^2 = (-1)^2).
Although the because parts are valid, the actual statement still go against basic laws used to define the math system, and thus, the proofs are false when applied to the mathematical system.
Awaken: And the point of that was..........?
Anyways on topic, a really good little story illustrating what happens when you use traditional arithmetic with an abstract concept like infinity is Hotel Ad Infinitum.
There is actually a mathematical paradox where you can make 1 =2. Take a sphere (not a physical sphere a maths sphere) and divide it into a finite number of pieces and you can reassemble it, only using translations and rotations, into 2 spheres of the same original size. Banach-Tarski paradox. Cool shit.
-spoon
infinity takes no space on the number line. It is not a real number, it is a concept. In "-∞ -5 -4 -3 -2 -1 0 1 2 3 4 5 ∞", infinity and negative infinity just represent a never ending succession of real numbers, not actual positions on the number line.Quote:
Originally posted by s00p
Plus, infinity can take more than one space on the number line (meaning it's either a really special happy number, or just not one at all)...
Dreamscape, nice work. Infinity is not a number, and no amount of zeros can add up to anything other than zero. You nailed it. You get a smily face. :D Counter arguments are much more intellectual, productive, and interesting than personal insults. Any kid in nursery school can come out of the blue and insult people.
I disagree with your point that this is not philosphy, however. We are talking about the philosophy of math, which coincides with the nature of reality. If it turns aout that 1 = 2, then we have to look at the nature of reality in a whole new way. I don't think anybody here actually agrees with the idea, but it is the concept we are talking about.
To me the universe created itself of a probabilty model from time.
probability 0=1 or any number, to a certian divisabilty for infinity, therefore we are not yet created, and never will end. Though we are created on the model of time, and the forces created by it, therefore we exist, and fluctuate to certain models to an unending evolution of a universe and not ourselves. Supersymmetry, symmetrical time. Heisenburg's uncertainty principle to someone else's extent. I take all thoughts. What do you think. :shock:
My point is that you can add anything to infinity, but it will still be infinity, and therefore not a number.Quote:
infinity takes no space on the number line. It is not a real number, it is a concept. In \"-∞ -5 -4 -3 -2 -1 0 1 2 3 4 5 ∞\", infinity and negative infinity just represent a never ending succession of real numbers, not actual positions on the number line.[/b]