Are older mathematics textbooks still "valid"? Being interested in learning rigorous calculus (as opposed to the content taught in AP Calculus and intro calculus courses in university), some textbooks mentioned quite often on the internet include Introduction to Calculus and Analysis, Vol. 1 by Richard Courant, Calculus, Vol. 1 by Tom Apostol, and A Course of Pure Mathematics by GH Hardy. These books are regarded as classics. 
My concern, however, is that they are rather old texts, particularly the one by GH Hardy. I do not want to learn from or purchase mathematics books which are inaccurate lest I develop any sort of false beliefs or misconceptions. My question is therefore as follows: are these books, and all relatively older (>5 decades) textbooks in general, sufficiently rigorous by the modern standards of pure mathematics?

Yes
Sometimes old textbooks use rather archaic language and slightly different terminology (like 1915 sort of age) but there is nothing "invalid" (except for maybe errors!) about them.
If it (correctly) proves a claim, that is that. Job done. 
(I love the fact I can buy old editions for a penny (without delivery) on Amazon, no other subject has this! They're always changing!)
