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I have 2 questions about theroms. Lets say i want to prove the therom:
x = math.floor(x+.5)
x10
If i said that x can represent any number and the statement can be true, since there are infinite different ways that it is true, and we tested the therom for the rest of the universe's time, and never came up with a number that disproved it, would it be considered that it is true?
Second question:
If we apply mathmatics to see when it is true, and when it is false, there are infinite true answers, and 10 ways to make it false. To get the percent it is true we can do:
(inf+10)/inf=100%
so the statement is true 100% of the time, and if we do the inverse of that:
10/(inf+10)=0%
so the statement is false 0% of the time, yet this is obviously not true. |
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morashJoin Date: 2010-05-22
Post Count: 5834 |
1. I guess you would consider it true since there is "no" possible way to disprove it.
2. inf + 10 would always be inf. Since dividing inf by inf would return one it is 100%. 10/inf would return an answer greater than zero, but because basic computers such as the one you and me use are incapable of getting a number such as 1e+-999 (yay science), it rounds it to 0, giving your answer. |
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I wasn't talking about using computers to get the answer of 10/inf.
My math over that calculation was:
.999repeating+(1/inf) = 1
.999repeating = 1
(1/inf) = 0
Is there something wrong with that? |
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morashJoin Date: 2010-05-22
Post Count: 5834 |
... Stop rounding if you want an accurate answer. |
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It's been proven(In base 9?+other ways) that .999 repeating equals 1...
To it's not rounding. |
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x = math.floor(x+.5)
x10
This is not true.
A counter example is x = 0.9.
Therefore the theorem is false.
As to your question of whether or not showing enough numbers is enough to prove a theorem - How many is enough? You would need a proof that `q` examples would imply the general truth of the theorem, and that `q` is dependant entirely on what your theorem is. |
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morashJoin Date: 2010-05-22
Post Count: 5834 |
x = .999...
10x = 9.999...
9x = 9
x = 1
x = .999...
5x = 5.666...8
x = 1.something
Hmm... I though .999... = 1 |
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Secondly:
Lack of disproof is NOT the same thing as proof.
Theorems may also be INDEPENDANT of axioms, which means there is no way to either prove or disprove the statement. The best example of this is the Euclidean parallel postulate; it must be taken as its own axiom because the system is (apparently) consistent without it (though the actual proof of consistency would be very very difficult [becuase proofs of consistency cannot eminate from the system itself, from Godel] and I don't think there is one yet) or with it. |
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@blue, the line:
x = math.floor(x+.5) makes so it only accepts integers, not decimals. So there is only 10 ways that the statement is not true. (For the used x value)
@morash, google it if you dont believe me :/
Also there is a thread some where on scripter that proves it...
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I have no idea what you're talking about.
You need to be clear when you're explaining things.
E.g., your statement should have been written something like:
"∀x∈ℕ → ⌊x+0.5⌋ = x"
"For all natural numbers x, the floor(x+0.5) = x"
We can clearly find a counterexample of x = 0.9.
Showing any amount of examples for a proof is not at all a proof and should convince no mathematician of the truth of the theorem, only that it's not necessarily false (e.g.,⌊x⌋ = 2x has a single example, and the lack of ability to demonstrate another would suggest that it's false).
Probabilities that something is true can be used at times, but only in sophisticated proofs and not so simply.
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OysiJoin Date: 2009-07-06
Post Count: 9058 |
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lombardo2Join Date: 2008-11-30
Post Count: 1603 |
Dividing by infinity is undefined. |
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@osi meant or... not and...
@tas, so i'm guessing i should at least take calc before i ever venture onto this subject again?
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jewelycatJoin Date: 2008-09-10
Post Count: 17345 |
No, I think you should take Algebra I before you attempt this... or use logic...
I'm not sure how this has anything to do with calculus, unless I missed something extremely important? |
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I'm in algebra 2 and i don't know half the things blue is talking about, and never seen the symbols he used.
Also, i saw nothing wrong with my first post, other then i said and instead of or. |
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S1xtyJoin Date: 2009-10-25
Post Count: 4491 |
Some infinities are larger than other:
inf1 = {...-2,-1,0,1,2...}, inf2 = {0,1,2...}
#inf1 = 2*(#inf2) |
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S1xtyJoin Date: 2009-10-25
Post Count: 4491 |
Any finite number divided by infinite is 0... Theoretically, because the limit of 1 number(y) divided by x as x approaches infinite is y/x so for example:
if the number is 7 and x is the infinite then 7/infinite - 1 = .0repeatingforever1
But if you were to make a table the larger and larger the finite denominator is then you could find the limit to be zero because the result would keep getting smaller and smaller |
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S1xtyJoin Date: 2009-10-25
Post Count: 4491 |
Ahhh, the wonders of calculus. |
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S1xtyJoin Date: 2009-10-25
Post Count: 4491 |
lim x --> inf (1/x) = 0 |
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S1xtyJoin Date: 2009-10-25
Post Count: 4491 |
lim x --> inf ((y ≠ inf ∈ ℝ)/inf) = 0 is more general |
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Infinity is not a number. It is an idea that has a few different meanings, each of which states that infinity doesn't technically have a fixed value (because if you were able to reach infinity it would go up higher and higher, because it is clearly not the largest number). You may as well be adding 10 to potato. |
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lombardo2Join Date: 2008-11-30
Post Count: 1603 |
"For all natural numbers x, the floor(x+0.5) = x"
We can clearly find a counterexample of x = 0.9.
But 0.9 ∉ ℕ or am I missing something |
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S1xtyJoin Date: 2009-10-25
Post Count: 4491 |
I know infinity isn't a value, that's why I used a limit. It just means it's larger than all real numbers and goes on forever, therefore my statement works. |
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S1xtyJoin Date: 2009-10-25
Post Count: 4491 |
Isn't a constant*
-- I hate the floodcheck -- |
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