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Aug 11, 2012 · Essentially, you gave the answer yourself: "infinity over infinity" is not defined just because it should be the result of limiting processes of different nature. I.e., since such a …

Similarly, the reals and the complex numbers each exclude infinity, so arithmetic isn't defined for it. You can extend those sets to include infinity - but then you have to extend the definition of …

Dec 25, 2017 · When we use straightforward approach, we get $$ \frac{\infty+1}{\infty} = \frac{\infty}{\infty} $$ In the process of investigating a limit, we know that both the numerator …

Infinity is not a natural number, or a real number: there should be no confusion about that. We can use infinity as the upper limit of an integral as shorthand to say that all the reals greater than …

Dec 18, 2012 · $\begingroup$ "Or that the infinity of the even numbers is the same as that of the natural numbers." - not necessary. This depends on your definitions. I would argue the infinity …

Infinity does not lead to contradiction, but we can not conceptualize $\infty$ as a number. The issue is similar to, what is $ + - \times$, where $-$ is the operator. The answer is undefined, …

May 14, 2017 · The infinity can somehow branch in a peculiar way, but I will not go any deeper here. This is just to show that you can consider far more exotic infinities if you want to. Let us …

Your title says something else than "infinity times zero". It says "infinity to the zeroth power". It is also an indefinite form because $$\infty^0 = \exp(0\log \infty) $$ but $\log\infty=\infty$, so the …

$\begingroup$ i am assuming from your answer that if a>1 then limit x--> + infinity or - infinity of a to the power x is = 0 $\endgroup$ – Zia ur Rahman Commented Oct 5, 2011 at 13:07

Jan 1, 2021 · Let us follow the convention that an expression with $\infty$ is "defined" (in the extended reals) if: when you replace each $\infty$ with any function/sequence whose limit is …