vinsan wrote:engineer wrote: If infinity^2 = infinity^3, then the limit of x^3/x^2 as x -> infinity should be 1. It clearly is infinity, not one, so infinity^2 is not the same as infinity^3.
I agree here....
Also Alap when u talk about infinity, the proofs need calculus based explanantion. Simple Algebra was never meant to deal with infinite sums.
God that is poor mathematics! What is the major (wrong) assumption you are playing with there to get your logic error? Just because a sequence is unbounded doesn't mean it can't interact with another unbounded series according to simple limit rules. Nor can you choose to ignore these rules. Your flaunting these limit series rules would allow limits of 1/x * lim x (meaning infinity times zero) are always equal to 1, spelling the death of mathematics.
The mistake made above falls into treating infinity like a number to push its implied properities onto all formulea generally and saying if they are infinite they are equal. Bad mistake. Infinity is not a number. Infinities can be 'sized' in number theory - meaning you rank limit series and growth rates of functions that generate infinities into certain classes of growth magnitude.
The question as stands is ambigous as I said. Does the author wish to proof and infinite 2 dimensional shape (square) is equalivalent to an infinite 3 dimension shape (cube) which it isn't. Does the author wish to show series x^2 and x^3 are unbounded and don't converge - this is true. Does the author wish to assume series x^2 and x^3 are not only unbounded and don't converge but are equal? Well this is planely false as the limit of x^2 / x^3 is zero whilst the limit of x^3 / x^2 is infinite, so they are obivously not equal.
I said it before - sloppy mathematics - sloppy precision in asking a vague, unclear question.
You can have sized infinities too which further let you be incorrect.
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