how much is exponential of infinity

Question

Hi..

 

Please inform me how much would be exponential of infinity

Answer 1

Interesting question. What power are you taking infinity to? Infinity is often represented with the symbol, ∞.

 

Any number to the zeroth power, other than 0, is 1, so ∞⁰ would be 1.

Any number raised to the first power is itself, so ∞¹ = ∞.

Multiplying any positive number (this is positive infinity, which is infinitely high, as opposed to negative infinity, which is infinitely low), other than 0, by infinity equals infinity, so ∞^x, where x > 0, would equal ∞.

Dividing any positive number, other than infinity (which is more of a concept than a number), by infinity, would yield 0. Raising a number to a negative power is like dividing 1 by it that many times, so ∞^-1 = 0, and ∞^x, where x < 0, yields 0.

 

To see the last point in action, take a calculator, and enter 1. Divide this by 2. You now have 0.5. Divide it by 2 again. You now have 0.25. If you keep doing this, the calculator will eventually show "0", although the actual result is not quite 0; it's just too small for the calculator to represent in its memory, so the calculator rounds it off to 0. You are effectively dividing 1 by a larger and larger number, which would be infinity, if you could press "=" an infinite number of times. 1 divided by x approaches 0, as x moves toward infinity. This is a brief introduction to the concept of a limit, which you will learn about in pre-calculus, if you advance that far in math.