in: ndobbs; ndobbs > 2017-01-24

Jan 26, 2017 11:48 PM
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What is it not? 9+elephant=?

What can you add together? Numbers, some matrices, vectors, polynomials, some functions...

So what is addition? Some operation on a class of things which gives you another element of that class. But so does subtraction, so addition should probably have some properties... like a+b = b+a and associativity and whatnot. Well, actually just those two (eg addition of whole numbers). But you may also want your class to have a zero element 0, so 0 + a = a... and maybe inverses as well, in which case you get an additive group (eg integers, real numbers, 3x3 matrices, etc).

Throw in multiplication as well and multiplicative identity and inverses and you get what the magic tractor turned into after it went down the road.

What can you add together? Numbers, some matrices, vectors, polynomials, some functions...

So what is addition? Some operation on a class of things which gives you another element of that class. But so does subtraction, so addition should probably have some properties... like a+b = b+a and associativity and whatnot. Well, actually just those two (eg addition of whole numbers). But you may also want your class to have a zero element 0, so 0 + a = a... and maybe inverses as well, in which case you get an additive group (eg integers, real numbers, 3x3 matrices, etc).

Throw in multiplication as well and multiplicative identity and inverses and you get what the magic tractor turned into after it went down the road.

Jan 31, 2017 8:40 PM
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Is adding puzzle pieces addition in the mathematical sense? Is there a puzzle space? Is it finite? Are there puzzle decimals?

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