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pratikdeoghare • yesterday at 4:38 PM • 1 reply • view on HN

It might help to point out to students that not all things called “number” in math are for counting/measuring.

Even before complex numbers, I was confused by negative numbers. Why negative times negative suddenly positive?

I spent time figuring that out. When complex numbers came I was ready. I knew they were not really numbers that would count something. And that they are just called numbers.

Replies

nh23423fefe • yesterday at 6:46 PM

    0 =[absorption] 0 * 0 =[def 0] (1-1)(1-1) =[distributivity] 1*1 + 1*-1 + -1*1 + -1*-1 =[def 1] 1 -1 -1 + -1*-1 =[eval] -1 + -1*-1 =[def 0] -1 + -(-1) =[def 0]  -1 + 1
therefore -1*-1 =[by left cancellation] 1