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- What is infinity divided by infinity? - Mathematics Stack Exchange
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
- What exactly is infinity? - Mathematics Stack Exchange
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 can be translated as " unboundedness ", itself derived from the Greek word apeiros, meaning " endless "
- Why is $\\infty \\cdot 0$ not clearly equal to $0$?
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 $\infty \cdot 0$ means strictly $\infty\cdot 0=0+0+\cdots+0=0$ per se I don't understand why the mathematical community has a difficulty with this
- One divided by Infinity? - Mathematics Stack Exchange
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 operators, to cope with that extended set And then, you need to start thinking about arithmetic differently
- definition - Is infinity a number? - Mathematics Stack Exchange
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 that it won't always act the way you've become accustomed to expect a number to act
- Types of infinity - Mathematics Stack Exchange
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 infi
- I have learned that 1 0 is infinity, why isnt it minus infinity?
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 viewpoint helps account for all indeterminate forms as well, such as $\frac {0} {0}$
- calculus - infinity times infinitesimal - what happens? - Mathematics . . .
Division of infinity by infinity as defined by these divergent geometric series will result in the limit (1) an infinity if the numerator has a smaller x, (2) an infinitesimal if the numerator has a larger x, (3) the finite value 1 if numerator and denominator have the same x
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