this post was submitted on 17 Apr 2024
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This only ever got handed down to us as gospel. Is there a compelling reason why we should accept that (-3) × (-3) = 9?
You can look at multiplication as a shorthand for repeated addition, so, for example:
In other words we have three lots of three. The zero will be handy later...
Next consider:
Here we have three lots of minus three. So what happens if we instead have minus three lots of three? Instead of adding the threes, we subtract them:
Finally, what if we want minus three lots of minus three? Subtracting a negative number is the equivalent of adding the positive value:
Do let me know if some of that isn't clear.
This was very clear. Now that I see it, I realize it’s the same reasoning why x^(-3) is 1/(x^3):
Thank you!