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  • 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 "
  • 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
  • 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
  • What is imaginary infinity, $i\lim\limits_ {x \to \infty} x = i\infty$?
    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 then turn to the complex plane The most common compactification is the one-point one (known as the Riemann sphere), where a single infinity $\tilde\infty$ is added
  • 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
  • Why is $1^ {\infty}$ considered to be an indeterminate form
    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 determine what happens in that form Hence, indeterminate form
  • 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
  • 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
  • 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 $\frac {0} {0}$
  • What is the square root of infinity and what is infinity^2?
    Thus both the "square root of infinity" and "square of infinity" make sense when infinity is interpreted as a hyperreal number An example of an infinite number in $ {}^\ast \mathbb R$ is represented by the sequence $1,2,3,\ldots$





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