Originally posted by Leonhard
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Originally posted by Cow Poke View PostThere's an extra "e" in the title. Vowels cost money!Last edited by 37818; 02-01-2015, 06:23 PM.. . . the gospel of Christ: for it is the power of God unto salvation to every one that believeth; . . . -- Romans 1:16 KJV
. . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3-4 KJV
Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1 KJV
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Originally posted by 37818 View PostOh, that is right, I ceep on frogetting that I cnat spel. You can remove the unnecessary e. Can you?The first to state his case seems right until another comes and cross-examines him.
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Originally posted by pancreasman View PostInfinity is NOT a number.
∞ - ∞ can be equal to 0. But did you know -∞=∞=∞i too.. . . the gospel of Christ: for it is the power of God unto salvation to every one that believeth; . . . -- Romans 1:16 KJV
. . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3-4 KJV
Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1 KJV
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Originally posted by Cow Poke View PostWhy.... it's .. um... GONE!!!!! ShaZAAAAAAAMMMMMM!. . . the gospel of Christ: for it is the power of God unto salvation to every one that believeth; . . . -- Romans 1:16 KJV
. . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3-4 KJV
Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1 KJV
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Okay, I'll try again:
Originally posted by Leonhard View PostIt depends on how you define what an infinite sum is, but simple progressive addition doesn't produce any convergence. There are other kinds of ways to define the summing of an infinite number of terms and interestingly they all give 1/4 for the above sum. Euler demonstrated this by defining a new type of infinite sum of terms as the following
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Originally posted by Paprika View PostIndeed. So again, and hopefully for the last time, if infinite sums can be defined as an operation yet not produce any convergence for some values over which it is defined, why not 1/0?
1/0 is undefined.
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1/0 could be given the output: NaN ∞ or ∞ NaN or error NaN ∞.
Then everybody can be happy or mad, or what ever.
But really what is the true answer? There is none. Or ∞. Or NaN. [NaN = "Not a Number"]. . . the gospel of Christ: for it is the power of God unto salvation to every one that believeth; . . . -- Romans 1:16 KJV
. . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3-4 KJV
Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1 KJV
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Originally posted by Leonhard View PostBecause a*0 = 0, for all a, no matter what a is. However in order to divide a number you need a*b = 1. And if you want to define 1/0 by the limit of 1/x, you'd want it to converge to one and only one result. You can do this for some of those irregular series, where using Ramanujan, or Abel summation you'd get some finite value... the same isn't true for 1/x for x->0, there you can get any result except that |1/x| -> infinity in all cases.
1/0 is undefined.
Do an inverse graph. 1 to the center being ∞. -1 is on one side, and 1 is on the to other. y = 5. The line crosses -∞ +∞ being the same point.. . . the gospel of Christ: for it is the power of God unto salvation to every one that believeth; . . . -- Romans 1:16 KJV
. . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3-4 KJV
Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1 KJV
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Originally posted by pancreasman View PostYou're using that symbol as if it were a number, but it isn't.. . . the gospel of Christ: for it is the power of God unto salvation to every one that believeth; . . . -- Romans 1:16 KJV
. . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3-4 KJV
Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1 KJV
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Originally posted by 37818 View Postx/(x + 1) = 1 for example.
(multiply both sides by (x + 1))
x = x + 1
(divided both sides by x)
x/x = x/x + 1/x
1 = 1 + 1/x
(subtract one from both sides)
0 = 1/x
(1/∞ = 0)
x = ∞
Here's how you'd do that equation properly. We desire to find an x belonging to the real numbers, fulfilling the following property you've given. This is typically written like
We'll do some algebraic manipulations here, since if the above expression is fulfilled by any x, then these following equations must be fulfilled as well, and be true.
Multiplying by (x+1) we get
However this implies that
Which is always false, but since we've only used valid algebraic operations, then our first sentence must be false, reducto ad absurdum. It becomes then its antithesis
And in fact its trivial to show that this result can be extended to any system of numbers where you can do multiplication and division like in the reals, complex numbers etc... called fields.
If you assert that the equation has a solution, any solution, then you assert that "0 = 1".
However its quite possible to show that as you make x larger and larger there is a definite limit to the equation
However notice the subtle distinction here. You were using infinity as an algebraic object, where as here its a symbol that means that we're constantly picking an ever larger x, and that the equation continously gets closer and closer... in fact arbitrarily close to 1. There's a very precise way of defining such a limit, but it would require a discussion of what continuity means. Safe to say that it avoids ever mentioning the word infinity, and the 'lim' with x -> ∞ just becomes a neat short hand for something that would otherwise be long, dry, repetitive and boring to write out.
OK. I respect your answers. I really do. I have come to some of these ideas that are not accepted as correct, for a long time. It does not mean I cannot learn. Or for that matter change my mind. Honestly, I dislike being wrong. To the best of my ability, as limited as it might even be [do to ignorance], I choose to believe what true, when I can understand it to be true.Last edited by Leonhard; 02-01-2015, 07:02 PM.
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Originally posted by Leonhard View PostThere's nothing dumb about Teal, but there definitely is something dumb about this post of yours.
Stop turning this thread into a discussion about evolution.
Do you know the meaning of "incredulous"?
No? I didn't think so.
Incredible.
K54
P.S. I despise Fundies.
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Originally posted by 37818 View Post1/0 could be given the output: NaN ∞ or ∞ NaN or error NaN ∞.
Then everybody can be happy or mad, or what ever.
But really what is the true answer? There is none. Or ∞. Or NaN. [NaN = "Not a Number"]
You can't divide by 0, so the result is not a number.
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