Comments on: Understanding Exponents (Why does 0^0 = 1?)

By: Kalid

Kalid — Tue, 25 May 2010 01:53:45 +0000

@Lee: Let me see if I get the question. With the base number 1 in the expandotron, we’re saying that after a unit of time, we have the same result. In fact, with 1 as the base, any amount of time will have the same result (no change). If we use imaginary numbers, strange things can occur, but that’s another article .

Turning back time for 1 second is asking “1 second ago, given this rate of growth, what was our number?”. Since the rate of growth doesn’t have any effect, the number is the same as the original. When you aren’t changing, 1 second ago you are still at your present amount.

In math terms, 1^x = 1 for any real x. Hope this helps!

By: Lee

Lee — Mon, 24 May 2010 18:14:56 +0000

What will happen if I place a base number of 1 to the expandotron, set it to zero growth and turn back time for 1 second?

By: Kalid

Kalid — Wed, 19 May 2010 05:53:41 +0000

@Alley: Great question! Here’s how I see it — exponential growth is about, well, growing stuff with multiplication! So we need to start with something to grow and compare. The reference point is 1, our original amount, and we see what we transform it into.

If we don’t do any changes, then our input = output, so we finish with 1.

Another way to think about it “times 3″ really means “1 times 3″, that is, start with your original amount and then scale it up. We often drop the implicit “1″, but when doing exponents it can help to explicitly talk about it. Hope this helps!