HP 48GX Collector’s Edition (merged) - please don't start two threads

[brouhaha]

(11-21-2023 08:30 PM)Johnh Wrote:  On the question of what 0^0 equals, obviously it's a conundrum, but I'm sure proper mathematicians are clear on what it should be. But here's my take, and the answer is 1:

If you say that 0^0 should be the limit of x^x as x approaches zero, then you can easily see the result heading towards 1 ie:.

And on the other hand, you can just as easily look at it as the limit of 0^x, as x approaches 0 from the right:

0^3 = 0
0^2 = 0
0^1 = 0
0^0 = ?

You can trivially construct cases that approach 0^0 from other directions, and yield other limiting values. This is why 0^0 is generally considered to be undefined.

There are good arguments for considering 0^0 to be1, but when doing so one should still be aware that it is actually a discontinuity, and that considering it to be 1 is an adopted convention and not literally "the true value" of 0^0.