Aug 11, 2012 · I know that $\infty/\infty$ is not generally defined. However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as-big infinity, for

Definition: Infinity refers to something without any limit, and is a concept relevant in a number of fields, predominantly mathematics and physics. The English word infinity derives from Latin infinitas, which …

Mar 25, 2011 · You never get to the infinity by repeating this process. Limit means that you approach the infinity but never actually get to it because it's not a number and cannot be reached. The expression …

Dec 18, 2012 · I understand that there are different types of infinity: one can (even intuitively) understand that the infinity of the reals is different from the infinity of the natural numbers. Or that the …

For infinity, that doesn't work; under any reasonable interpretation, $1+\infty=2+\infty$, but $1\ne2$. So while for some purposes it is useful to treat infinity as if it were a number, it is important to remember …

This resolves your problem because it shows that $\frac {1} {\epsilon}$ will be positive infinity or infinite infinity depending on the sign of the original infinitesimal, while division by zero is still undefined. This …

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 the arithmetic …

May 28, 2017 · Note that stating the reverse is more delicate, since we use to give a sign to infinity. Both $\lim\limits_ {x\to+\infty} \frac 1x=\lim\limits_ {x\to-\infty}\frac 1x=0$ but we cannot conclude $\frac …

This "$1^\infty$" (in regards to indeterminate forms) actually means: when there is an expression that approaches 1 and then it is raised to the power of an expression that approaches infinity we can't …

Mar 16, 2015 · Why is it that e raised to the power of negative infinity would equal 0 instead of negative infinity? I am working on problems with regards to limits of integration, specifically improper integrals...