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 :)
$\endgroup$2 Answers
$\begingroup$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).
$\endgroup$ $\begingroup$Consistency can also be found in statistics: it means that as your sample is getting bigger,your estimator is becoming better and better.
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