7 ms·
> How would you explain to a 10-year old why 3^0 = 1 You draw the line 3^x. It "passes through" 1 when x = 0. So don't think about the point, think about the
by parallel 15y ago
> How would you explain to a 10-year old why 3^0 = 1
You draw the line 3^x. It "passes through" 1 when x = 0. So don't think about the point, think about the line. It's not rigorous but it's intuitive.
http://fooplot.com/index.php?q0=3^x http://fooplot.com/index.php?q0=3^x
edit: added link and fixed typos
- vessenes 15y agoThis is precisely the problem, though. The same 10 year old draws two lines: 0^x, and x^0. They clearly do not meet.
- parallel 15y agoYeah, I was just talking about the easier concept of x^0. Going the other way, 0^x it makes a lot less sense to me. I know that for all positive x, 0^x = 0. That it pops up to 1 at the origin means the thing is not smooth so drawing lines isn't going to help us. Plotting z = y^x could be interesting but we're going to see asymptotic behaviour at x = y = 0 (when going in the x direction). So no easy wins there.