First, ∞ is *not* number. It’s symbol for infinity. For example in the natural numbers set **N** (the set of all positive integers), there are infinite number of numbers, but none of them is ∞.

But now to the example…

What is 1^{∞}? Layman probably would say that that’s 1, but according to mathematicians 1^{∞} is not defined; we can’t say (at least by our understanding on infinity we have at the moment) what it is.

But what if we get ”close” to 1^{∞}? Let’s examine following:

From arithmetic operations in infinity we remember, that

So what we have at the first limit sentence is ”1^{∞} ” and for

an exact value can in fact be determined! It’s the Napier’s number *e*, that’s an irrational number i.e. its decimal representation is infinite. It’s approximately 2.718281828459.

What I presented here, I came familiar with on my first university year.

On Infinity on Amazon

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Posted by Markus in Mathematics Tags: 1 power infinity, infinity, Mathematics, Napier's number e, powers