There is a subset of Q that is canonicaly isomorph to Z. Probably the distiction is too technical unless you want to do some weird advanced algebra. (Note that in most weird advanced math the distiction doen't matter.)
So in most case, mathematicians and non mathematicians just write Z ⊂ Q and live happily ever after. But if you get supertechnical you should use scare quotes Z "⊂" Q or to look more proffesional Z ↪ Q (because tha inclusion is an injective funcion, and sometimes it's useful to think aboout it as a function.).
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To add some confussion: Imagine that you buy in the supermarket a copy of Z that is green and another copy of Z that is red.
1(red) + 2 (red) = 3(red)
1(green) + 2(green) = 3(green)
(If I get super technical, I have to define a +(red) operation and a +(green) operation. And probably also a =(red) and =(green) as the article discuss.)
Are they the same Z or just canonicaly isomorph or it doen't matter?
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To add even more confussion: You have a copy of abstract Z and a copy inside the rational written as n/1:
1 + 2 = 3
1/1 + 2/1 = 3/1
Are they the same Z or just canonicaly isomorph or it doen't matter?
So in most case, mathematicians and non mathematicians just write Z ⊂ Q and live happily ever after. But if you get supertechnical you should use scare quotes Z "⊂" Q or to look more proffesional Z ↪ Q (because tha inclusion is an injective funcion, and sometimes it's useful to think aboout it as a function.).
---
To add some confussion: Imagine that you buy in the supermarket a copy of Z that is green and another copy of Z that is red.
1(red) + 2 (red) = 3(red)
1(green) + 2(green) = 3(green)
(If I get super technical, I have to define a +(red) operation and a +(green) operation. And probably also a =(red) and =(green) as the article discuss.)
Are they the same Z or just canonicaly isomorph or it doen't matter?
---
To add even more confussion: You have a copy of abstract Z and a copy inside the rational written as n/1:
1 + 2 = 3
1/1 + 2/1 = 3/1
Are they the same Z or just canonicaly isomorph or it doen't matter?