What does consistency mean in Mathematics?

Question

What does consistency mean in Mathematics?

Does the meaning vary as per the context?

If yes, than can you give some examples?

PS: I'm not sure what is the correct tag for this question, please someone edit it. Thank you so much :)

Answer 1

It does depend on context, but basically it means "does not lead to contradictions".

In mathematical logic, a set of axioms is consistent if you can't use them to prove a contradiction.

In algebra, a set of equations is consistent if they do not imply something impossible, like $0 = 1$ (which is really just a special case of the above example, where the given equations are added as axioms in addition to the rules of algebra).

Answer 2

Consistency can also be found in statistics: it means that as your sample is getting bigger,your estimator is becoming better and better.