Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20070524 19:05:13
Power of 0I am having trouble understanding how x°=1, for any value of x. Last edited by Daniel123 (20070524 19:05:44) #2 20070524 19:14:29
Re: Power of 0well, easiest way to think about is to look at it like a series: as you go down the series, you divide by n, n/n = 1 as you go up the series, you multiply by n, 1/n*n = 1 example there, as you go down, you divide by 2, 8>4>2>1>0.5>0.25 same going up, the only number that makes sense is 1. the only time it doesnt really apply is in 0^0, but to keep it consistent, we say that 0^0 = 1 aswell, although often, youll just see it as undefined aswell. Last edited by lucadeltodesco (20070524 19:16:41) The Beginning Of All Things To End. The End Of All Things To Come. #3 20070524 19:21:52
Re: Power of 0This 0^0 thing really confuses me. It needs to be 1 to be consistent with Luca's sequence, but then it breaks this one: Why did the vector cross the road? It wanted to be normal. #4 20070524 19:29:10
Re: Power of 0Ok so i can now see why x°=1 #5 20070524 19:56:26
Re: Power of 0Im just wondering, in other bases, e.g. base6, would 0 have the same value? I find it imposible to understand other bases.... and just out of curiosity, why did we choose base10? Would mathematical rules still be the same if other bases were used? #6 20070524 23:36:14
Re: Power of 0To understand other bases I made a simple little "base counting" flash thingy here: Binary, Decimal and Hexadecimal Numbers "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #7 20070524 23:40:36
Re: Power of 0Typically, 0^0 is left undefined. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #8 20070524 23:48:51
Re: Power of 0Thanks both of you it has really helped my understanding #9 20070525 00:11:15
Re: Power of 0
The exponential series equates it to one, which I believe is the limit, rather than zero. #10 20070909 22:33:25
Re: Power of 0Ignoring official laws, I'd say x^0 where x is a number, is typically 0, because take a. a multiplied 0 times is: I shall be on leave until I say so... 