Infinity and Its Symbol

wise man contemplates infinity

In mathematics an unimaginably large value is said to be at infinity or is said to be infinity. For the moment, let us consider such a value to be positive. That is, think of an x number line with the origin, or zero, on it. In your imagination have it extend from zero to the right forever. One could say that infinity is at the end of that line. Except that line has no end. It goes on without end.

So, how far away to the right of zero is positive infinity? Well, if you started at the origin and spent your whole life running toward infinity at a million miles per hour, and somehow miraculously lived for a million lifetimes, at the end of all of that you would be no closer to infinity than when you started. That puts infinity very far away indeed. The symbol for this value looks like this:

This symbol is often read 'positive infinity'. Just like for normal numbers, the positive sign on infinity can be implied or 'invisible'. Therefore, this symbol has the same meaning:


What about the symbol for negative infinity, that value which is forever distant to the left of the origin? That symbol looks like this:


One could think of the positive infinity symbol as a variable with a value that is larger than any other positive number or that is less, in the case of negative infinity, than any negative number.

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