4 ms·
Not sure if I agree with the statement that "=" is used for definitions. It's true meaning is to simply state that two things are equal. I can see where the con
by contravariant 11y ago
Not sure if I agree with the statement that "=" is used for definitions. It's true meaning is to simply state that two things are equal. I can see where the confusion comes from since mathematicians have a tendency to just state "Let x = 2kj", instead of the more explicit "Let us assume that the statement 'x = 2kj', is true". It's important to note the distinction though, since introducing a new variable by simply stating it's properties is more powerful than just defining it to be equal to something. For instance it's equally valid to define a symbol x by simply stating "Let x∈A". This is used quite a lot since anything you can then prove about "x" must automatically be true for all elements of A.
- arsenide 11y agoI like the idea of using the compound symbol ":=" for "is defined to be". So, you can say something like "For x∈A, y := 2x". When I take math notes, it helps a lot using this shorthand. I'm able to remove some ambiguity between what is and is not a definition.
- contravariant 11y agoI definitely agree with the use of ":=", but "=" simply doesn't mean the same thing. For example, the similar statement "For x∈A, y = 2x" could even be interpreted as using y to define x.
- mattdesl 11y agoI'm working on improving that section; would be great if you could chime in here: https://github.com/Jam3/math-as-code/issues/17 https://github.com/Jam3/math-as-code/issues/17
- arsenide 11y agoI don't understand -- you say "=" and ":=" are not the same thing, but give an example where they act the same? Practically speaking, using ":=" removes any doubt when quickly skimming over old notes. It is nice to be able to easily separate what is defined and what is asserted in each of dozens of statements.