We state that a established $A$ is finite if and provided that there exists some $kinmathbb N$ these kinds of that there exists $fcolon Ato ninmathbb Nmid nCookie Settings
Bhaskar VashishthBhaskar Vashishth 11.6k55 gold badges4444 silver badges9393 bronze badges $endgroup$ one four $begingroup$ Not all of that convincing, considering that there are lots of programs such as infinite numbers, so Probably the reply must be “it relies upon which infinity you take”. Other responses elaborate this. $endgroup$
10 $begingroup$ @saadtaame: because looking at Wikipedia won't include inquiring other people to complete Focus on your behalf. $endgroup$
without the need of working with Taylor series. extra explicitly with out using calculus. how do we know if a purpose may be expressed as collection or not ?
Lets try this devoid of Taylor collection. A functionality that could be expressed by a true energy sequence is known as actual analytic. All of that is required is that all derivatives are bigger than or equal to $0$. Plainly this retains for $e^x$.
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If we subtract every one of the non-computable infinite sequences in the established, does cardinality alter? three
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(the principal exception I realize of would be the prolonged hyperreal line, that has lots of infinite numbers obeying the 'typical' legal guidelines of arithmetic, along with a pair of further figures we simply call $+infty$ and $-infty$ which have the most important magnitude of all infinite numbers, and don't obey the 'regular' rules of Infinite Craft arithmetic)
– Qiaochu Yuan Commented Aug 21, 2012 at 23:forty six six $begingroup$ @saadtaame, I believe what Qiaochu is attempting to speak you is usually that if you can find some facts in Wikipedia, not to mention in hundreds of thousands of other sites in the web, Then you really shoud to start with check out to master there a few points regarding your individual concern, lest men and women Consider you happen to be far too lazy to do that by on your own . $endgroup$