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You get the same answer if you only use '+', but you may get a different answer if you use 'x', that was my point. In other words, once you have a "canonical" a
by darkmighty 12y ago
You get the same answer if you only use '+', but you may get a different answer if you use 'x', that was my point. In other words, once you have a "canonical" addition table for the elements of a set, there are many multiplications tables to choose from which "extend" the addition in a straightforward way.
Sorry not very knowledgeable on this stuff so it took a long detour.
- pmalynin 12y agoOk, no problem. However once again that is not true and it has to do with the underlying mathematical structure (for which + and * are defined). Here is an easy way to think about: Imagine a filing cabinet with 3 drawers. Drawer 1 has papers "0", "3", "-3", "6", "-6" and so on. Drawer 2 has papers "1", "4", "-2", "-5" and so on. Drawer 3 has papers "2", "-1", "5", "-4", "8" and so on. So how do we add the two papers? Well you simply look at the numbers so "1" and "2", for example, and you add them -- we get "3". Now where do we put it under? Drawer 1, as it has the "3" in it. Or say we want to multiply "4" and "2", we just "multiply" and get "8", so it goes into Drawer 3. Now I say Drawer 1 should be labeled "0", Drawer 2 "1", and Drawer 3 "-1". But you might call me a sinner and a liar and say that Drawer 3 is "2". But it doesn't matter! "-1" and "2" are both equally valid and can be used as labels. Heck, you could even call it "8".
- darkmighty 12y agoOh so multiplication actually works nicely! Neat, thanks for the explanation.