(September 14, 2016 at 11:38 am)Whateverist Wrote:(September 14, 2016 at 11:28 am)RozKek Wrote: I've really liked math since 6th grade, and very recently I've started getting into it even more, at the start of our first math lecture this season my teacher came to me and my friend and slid the mathematics challenge book to us and walked away. I really need to get started with it, it seems really interesting, I haven't read much about proofs, but I'll try to get into it.
I'm going to start with why the heck x^0 equals 1.
That seems like more a matter of definitions and making conventions compatible.
If you think of x^3: as 1•x•x•x
and x^2 as: 1•x•x
and x^1 as: 1•x
then x^0 should be simply: 1
Note that 3 isn't a factor in x^3 any more than 2 is a factor in x^2. So there is no reason 0 should be a factor in x^0, the usual worry. Note that every factorization includes 1 trivially. x^1 does too. x^0 = 1 because there are no factors of x in it at all. But every factorization includes 1, trivially.
There are better justifications for this, but I found this way the most satisfying to students.
heya, hoya, hoo, I'm not reading this until I give it some thought myself
but thanks, I'll read this when I'm done crying
