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November 24th, 2013, 11:15 AM   #21
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Re: Zero-infinity number arrangement based on number size.

of course it is an element of "undefined infinity", and it explains its idempotency, it is not a number at all (but yes element!) simply because numbers don't behave like
a+ b = b; a= b-b ; a=0; b=undefined
But, tell me one thing, for example we have 2 functions y=x+2 and y=x; and we want to find difference between them at infinity.
It is obvious that it will always be x+2 - x = 2; but having x replaced with infinity we will have (inf+2 - inf) and inf-inf=undefined and we don't get an answer.
(you would probably send me to the theory of limits and etc. the thing i want to find out is why infinity was made this way, what was the reason for this?)
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November 24th, 2013, 04:31 PM   #22
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Re: Zero-infinity number arrangement based on number size.

Quote:
Originally Posted by Omnispark
But, tell me one thing, for example we have 2 functions y=x+2 and y=x; and we want to find difference between them at infinity.
It is obvious that it will always be x+2 - x = 2; but having x replaced with infinity we will have (inf+2 - inf) and inf-inf=undefined and we don't get an answer.
You could say similar things about (x - 1)/(x^2 - 1) and the value x = 1.
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November 25th, 2013, 11:18 AM   #23
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Re: Zero-infinity number arrangement based on number size.

but 1 is defined. 1-1=0, 1/1=1 etc.
i dont understand how simple operations over infinity can be undefined, how int the world lim(x->inf): x-x would not be solved if x is substituted with infinity, when we know that all of the x'es are approaching the same infinite number. but wait sameness is expressed through x'es, thats why it always comes down to simplification of expressions, because it is much easier to work with variables than numbers, because x/x=1. and x-x=0; no weird infinities and zeros)

theres interesting thing: lets substitute 1 with 1-e, like x is approaching 1 from the side of positive infinity, (e is still incredibly small value = 1/inf)
1-e-1 /(1-e)^2-1 =
e/1-2e+e^2-1 =
e/2e+e^2 ;
since e^2 is infinitely times smaller than e, it can be merged with 2e, =>
e/2e =
1/2;
on the opposite side, dealing with infinity we can merge all lower powers of infinity up to the highest one. 9inf^2+3inf+3 = 9inf^2
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November 25th, 2013, 06:38 PM   #24
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Re: Zero-infinity number arrangement based on number size.

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Originally Posted by Omnispark
but 1 is defined. 1-1=0, 1/1=1 etc.
i dont understand how simple operations over infinity can be undefined, how int the world lim(x->inf): x-x would not be solved if x is substituted with infinity, when we know that all of the x'es are approaching the same infinite number.
Perhaps my hint was not obvious enough. Google [removable discontinuity].
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November 28th, 2013, 03:11 AM   #25
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Re: Zero-infinity number arrangement based on number size.

Well, somehow i was unaware about it.
I think you guys have given me enough answers to obsess on, thank you very much!
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November 28th, 2013, 07:01 PM   #26
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Re: Zero-infinity number arrangement based on number size.

Great, good luck!
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