кошмар в головах народных

[juan_gandhi]

Вот тут устроил дискуссию на тему "что есть уравнение". И в учебнике, и в вики пишут, что "12 = 5+7" - это уравнение.

Это не уравнение. Это числовое равенство. Верное числовое равенство.

Печально, короче. И ведь не переубедишь эти толпы педагогов, которые все лучше знают. 

Аяяй.

На вики дискуссия.

Comments

[sassa_nf]

Logically there is a difference.

a=b is a proposition. (propositional equality)

Some of these can be decided to be:

0. definitional equality (0 = 0; by definition)
1. computational equality (2+2 = 4; by applying reductions, eg δ-reduction here)
2. judgemental equality (a+b = b+a; by constructing a chain of judgements, in the end composed from axioms)

0=1 - a proposition of equality, which can be shown to be judgementally false (from axiom 8 - ∀ x, S(x) = 0 is false).

[thedeemon]

The question is, in which case such proposition is called an equation.

[sassa_nf]

...always?

https://ncatlab.org/nlab/show/equation

[thedeemon]

Works for me. You just didn't mention this above, so the reply wasn't answering the question.

[juan_gandhi]

Thank you.