OpinionatedCyborg
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Math is the tool of the devil.
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Math is hard
- Thread starter Squirrel Killer
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Take calculus for the love of god. You'll fail but at least you might have a chance of having a clue of what you're talking about.Red Scarlet said:
Comments like this happen all the time in this board, but it usually pertains to gaming where it's more opinion then fact. Math is all about facts, about truth and non-truth, so you can't make comment like these without being completely, inarguably wrong.
OpinionatedCyborg
Member
We don't like what we don't understand in fact it scares us and this problem is mysterious at least. Has Zeno's paradox been mentioned yet?
LizardKing
Member
ok, is .9999.... the same thing as writing: .9 and .99 and .999 and .9999 and .99999 and .999999 continuously forever?
but how does it converge to 1 if you continually just add another 9? While you would never be able to fit another number between .999... and 1 at the same time you would also never fully reach one because you would still have an (literally) infinitely small missing piece.Trident said:
If I gave you something that weighed on a scale to an infinite decimal place and the thing I gave you weighed .999... grams you would never be able to say I gave you something that weighed 1 gram without approximating.
I think a big problem here is that some people think that 1/3 and .333... are some naturally-evolving "numbers" that exist that mankind has harnessed for his own personal use.
In fact, they are just NOTATIONS of a number. 1/3 means nothing to nature -- it is just a notation that humans made up to signify something split into 3 equal pieces.
In the same way, we made up .333... as ANOTHER notation of the same number.
You don't have to prove that 1/3 = .333... because we made them up to be.
If we wanted to, we could have made up the notation GEORGEWASHINGTON<3 to also mean 1/3 and we would be having this argument with you asking me to prove that 1/3 = GEORGEWASHINGTON<3 .
But there's no proof because we made them up to be the same thing. They are just expressions of the same CONCEPT, and the concept is what's important here.
In fact, they are just NOTATIONS of a number. 1/3 means nothing to nature -- it is just a notation that humans made up to signify something split into 3 equal pieces.
In the same way, we made up .333... as ANOTHER notation of the same number.
You don't have to prove that 1/3 = .333... because we made them up to be.
If we wanted to, we could have made up the notation GEORGEWASHINGTON<3 to also mean 1/3 and we would be having this argument with you asking me to prove that 1/3 = GEORGEWASHINGTON<3 .
But there's no proof because we made them up to be the same thing. They are just expressions of the same CONCEPT, and the concept is what's important here.
OpinionatedCyborg
Member
LizardKing said:
It's something you can't visualize IMO since we don't really understand "forever". THis is really a debate between those thinking "but there will always be a small difference between 1 and .999...; no matter how close it gets to 1, it never quite gets there" and those who have a little calculus knowledge.
Here's the simplest way I can put it.
1.000...
- .999...
= .000...
borghe said:
dude, i can't derive all of the laws of mathematics. If you want to get a book, read the axioms upon which the system is based, and build it up from there, BE MY GUEST. But barring that, you can't really use intuition to override what's been discovered. You were saying you can't use finite arithmetic with infinite numbers, but the truth is you can't use finite THINKING with infinite numbers.
The way a continuous number line works IN MATHEMATICS is that every number has an infinite amount of numbers between them. There's no "infinitely small space," there's no space. There's only numbers. Either there is an infinite number of numbers between two of them, or they are the same number. There's no debate within mathematics.
LizardKing
Member
well i took calculus and in that and throughout all my math classes (including calc physics) i was told that they are not the same number, at least when making calculations and whatnot. that does not mean there isn't a certain constraint, rule or theory in which to work in that makes them the same number however.
Squirrel Killer
Member
Man, I'm glad I never took Calculus, because it obviously make you insane. 
Guys, an infinitely small difference is still a difference, i.e. not equal. Close enough to substitute one for the other, sure, but equal, no.
Guys, an infinitely small difference is still a difference, i.e. not equal. Close enough to substitute one for the other, sure, but equal, no.
You don't need Calculus; you just need logic.Squirrel Killer said:Man, I'm glad I never took Calculus, because it obviously make you insane.
Guys, an infinitely small difference is still a difference, i.e. not equal. Close enough to substitute one for the other, sure, but equal, no.
There's no such thing as "an infinitely small difference." If you can't define it, it does not exist.
LizardKing
Member
Mihail said:
Squirrel Killer said:Man, I'm glad I never took Calculus, because it obviously make you insane.
Guys, an infinitely small difference is still a difference, i.e. not equal. Close enough to substitute one for the other, sure, but equal, no.
Man, I'm glad I never took a chemistry class, because water and sodium don't explode on their own, so they obviously won't explode from just touching each other. Watch, I'll just throw this huge block of sodium into the tub with meOHMYGODITBURNS
INFINITY IS NOT AN INTUITIVE CONCEPT. YOU CAN'T JUST SIT BACK, WIDDLE WOOD, TALK ABOUT LIFE EXPERIENCES, AND EXPLAIN HOW IT WORKS
OpinionatedCyborg
Member
.999... = 1 is like the properties of light.
This is an interesting read for everyone here, including cocky Trident 
http://www.math.toronto.edu/mathnet/answers/infinity.html
http://www.math.toronto.edu/mathnet/answers/infinity.html
LizardKing
Member
I think that is where the disagreement stems
Shompola said:This is an interesting read for everyone here, including cocky Trident
http://www.math.toronto.edu/mathnet/answers/infinity.html
That was an interesting read. I don't mean to give off the impression that I know everything there is to know about math. I certainly don't. I just get annoyed when people try to act as if math is some intuitive thing they can just think about for 10 minutes, relate to something they've seen, and explain away. If you've never taken calculus, and you want to talk about infinite series, then study first. You don't see me making comments about international economics just because I bought dinner once in Mexico.
Claiming mathematical laws are "bullshit" or derived by "throwing your hands up in the air" is some of the most disrespectful, ignorant, and aggrivating things somebody can do. Show some respect.
but I think that article did a great job of showing support that it is a matter of perspective. .999... = 1 as long as you accept that infinity doesn't exist and eventually there will be convergence. which is ironic to the degree that you are using an infinitely repeating series of numbers but by default using the fact that infinity doesn't exist.Trident said:
borghe said:
This is where limits come in. Since I'm obviously not capable of explaining things well, here are some links:
http://en.wikipedia.org/wiki/Infinite#Infinity_in_real_analysis
http://en.wikipedia.org/wiki/Limit_of_a_sequence
http://en.wikipedia.org/wiki/Series_(mathematics)
If you can read and understand them, and still think that there is some uncertainty of perpsective involved, then I don't know what to say.
[Edit]
Ah-ha! Here's a great example. It can't be understood without a grasp of calculus, but those links above should help. This is an adaption of: http://en.wikipedia.org/wiki/Geometric_series#Infinite_geometric_series
take the infinite series 9 * 1/10^n for n = 0 to lim as n approaches infinity
this is the same as 9/10 + 9/100 + 9/1000 + ...
this is the same as .9 + .09 + .009 + .0009 + ...
this is the same as .999...
this is the same as 9/10 * the geometic series where x = 1/10 (see above link)
the geometric series is equal to 1/(1-x)
therefore, .999... is equal to 9/10 * 1/(1- 1/10) = 9/10 * 1/(9/10) = 9/10 * 10/9 = 1 !!!!!
OpinionatedCyborg
Member
Add this one: http://en.wikipedia.org/wiki/Zeno's_paradoxesTrident said:
Red Scarlet
Member
Whatever, LakeEarth. I never claimed to be a math genius, that's how I heard it (that it is an accepted approximation), and well, sorry to piss you off so much. There are still many theories though, it isn't all black and white for math (I think). But hey, who cares, I'm a dumbshit and you're a bad motherfucker. Go you, you awesome genius, you. I'd definitely fail calculus though, and I really don't care. :lol
It's all semantic (and here's the keyword) bullshit. It's all trickery to make someone accept one 'proof' and then they have to accept the other. As numbers, I don't find them the same. You do. You have your logic, I have mine, the world moves on. This topic always brings out the snooty assholes. It's like an abortion debate for math nerds.
Math sucks.
Possibly Nietzsche.
It's all semantic (and here's the keyword) bullshit. It's all trickery to make someone accept one 'proof' and then they have to accept the other. As numbers, I don't find them the same. You do. You have your logic, I have mine, the world moves on. This topic always brings out the snooty assholes.
It's like an abortion debate for math nerds.Math sucks.
LakeEarth said:
Possibly Nietzsche.
x = 0.999....
10x = 9.999...
10x - x = 9.999... - 0.999
9x = 9
x = 1
Is proof that 0.999... = 1 only if you assume that it also = 0.999... as a completely seperate number....... Otherwise the equation wouldn't work.........
x = 0.999....
10x = 9.999...
10x - x = 9.999... - 0.999
9x = 8.999...
You see.......... If 0.999... = 1 then doesn't it make sense to subtract 1 from 9.999... instead of .999... itself? With that you are pretty much admitting that this theory doesn't work out without the other. :-/ (oh btw I know this one isn't going to go down to well with those who have complete faith in math and all it's greatness ^^; )
What it all comes down to is the fact that math is man made...... Made made stuff is flawed...... It's called human error........ It's the same as trying to explain time....... When did it start? It must have started somewhere, but, where? There is no way to define this.......... It's also the same as trying to explain where the universe came from or where it ends....... If there is an end what's outside of it? These limits that humans create are the same as the limits used in math...... They can't possibly exist otherwise there would be nothingness.......... The concept of something that is infinate but with limits makes no sense it completely destroys the idea......... Basically 0.999... is just that......... 0.999... 1 is also 1........ But as math is a man made thing it must follow man made rules which state that 0.999... = 1 as without this math as a whole isn't complete........ It would mean there is no such thing as 1/3 in a decimal form.....
Hmmm so yeah, math is flawed, science is flawed and yeah religion is flawed as well...... Pretty much everything man made is flawed.............. I guess we can all be happy that language isn't....... :-/ Or is it...... *shrugs*
10x = 9.999...
10x - x = 9.999... - 0.999
9x = 9
x = 1
Is proof that 0.999... = 1 only if you assume that it also = 0.999... as a completely seperate number....... Otherwise the equation wouldn't work.........
x = 0.999....
10x = 9.999...
10x - x = 9.999... - 0.999
9x = 8.999...
You see.......... If 0.999... = 1 then doesn't it make sense to subtract 1 from 9.999... instead of .999... itself? With that you are pretty much admitting that this theory doesn't work out without the other. :-/ (oh btw I know this one isn't going to go down to well with those who have complete faith in math and all it's greatness ^^; )
What it all comes down to is the fact that math is man made...... Made made stuff is flawed...... It's called human error........ It's the same as trying to explain time....... When did it start? It must have started somewhere, but, where? There is no way to define this.......... It's also the same as trying to explain where the universe came from or where it ends....... If there is an end what's outside of it? These limits that humans create are the same as the limits used in math...... They can't possibly exist otherwise there would be nothingness.......... The concept of something that is infinate but with limits makes no sense it completely destroys the idea......... Basically 0.999... is just that......... 0.999... 1 is also 1........ But as math is a man made thing it must follow man made rules which state that 0.999... = 1 as without this math as a whole isn't complete........ It would mean there is no such thing as 1/3 in a decimal form.....
Hmmm so yeah, math is flawed, science is flawed and yeah religion is flawed as well...... Pretty much everything man made is flawed.............. I guess we can all be happy that language isn't....... :-/ Or is it...... *shrugs*
The 10x - x "common sense proof" is hardly a formal proof to use in a criticism of mathematics.
If you are going to examine 0.999... properly, I'd imagine(as I'm no expert on this) it's going to be through something like comparing 1 to limit of a series which approaches 1 as precision approaches infinite. In the end, it could be said that since the only difference between 1 and 0.999... is a surreal number, in real number terms they are equal.
If you are going to examine 0.999... properly, I'd imagine(as I'm no expert on this) it's going to be through something like comparing 1 to limit of a series which approaches 1 as precision approaches infinite. In the end, it could be said that since the only difference between 1 and 0.999... is a surreal number, in real number terms they are equal.
Great King Bowser
Property of Kaz Harai
Set theory 
B = {X : X is an element of N and x < 5 and x^2 > 30}
Er, I missed the lecture. :lol
Any help?
Edit - Oh I'm guessing it's an empty set. Bastards.
B = {X : X is an element of N and x < 5 and x^2 > 30}
Er, I missed the lecture. :lol
Any help?
Edit - Oh I'm guessing it's an empty set. Bastards.
Great King Bowser
Property of Kaz Harai
Use simple induction to show that n < n squared for all positive integers n greater than or equal to 2. State clearly your basis, induction hypothesis, and what you need to show given the induction hypothesis.
LOOK A NUMBER THEORY JOKE
every odd is prime, a series of proofs:
the mathematician's proof:
3 is prime, 5 is prime, 7 is prime, so by induction it must be true!
the physicist's proof:
3 is prime, 5 is prime, 7 is prime, 9 is experimental error, 11 is prime, 13 is prime... we can't find any experimental counterexamples so i guess it's true!
the engineer's proof:
3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime, 13 is prime, 15 is prime...
MY OWN APPENDIX
the computer scientist's proof:
primes are indivisible so by definition it's true!
every odd is prime, a series of proofs:
the mathematician's proof:
3 is prime, 5 is prime, 7 is prime, so by induction it must be true!
the physicist's proof:
3 is prime, 5 is prime, 7 is prime, 9 is experimental error, 11 is prime, 13 is prime... we can't find any experimental counterexamples so i guess it's true!
the engineer's proof:
3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime, 13 is prime, 15 is prime...
MY OWN APPENDIX
the computer scientist's proof:
primes are indivisible so by definition it's true!
Great King Bowser said:
1) base case, n < n^2
n = 2
2 < 2^2
2 < 4
TRUE for n = 2
2) lets assume it is true for n = p, this is our induction hypothesis
lets prove for n = p+1, induction step
p < p^2 wich can be rewritten as
p + 1 < p^2 + 1
if we can show that p^2 + 1 < (p+1)^2, then we also show p + 1 < p^2 + 1 < (p+1)^2
p^2 + 1 < (p+1)^2 =>
p^2 + 1 < p^2 + 2p + 1 =>
0 < 2p
TRUE for n = p+1
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