Just a thought came in my mind , i understand the original def of epsliom delta version of limit . Why cant the limit definition be based on" for every delta there exits epsilon thing such that..."? Why the mathematicians give def for "every epsilon there exists delta such that..", was there some kind of contradiction in that def for some functions where it was not valid? Hence the epsilon to delta was selected ?
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3Are you sure you understood the definition? – Riquelme Apr 03 '21 at 12:49
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2Or maybe this will, https://math.stackexchange.com/questions/3554346/in-the-epsilon-delta-definition-what-is-wrong-if-i-said-given-delta-there-ex – Aditya Prakash Apr 03 '21 at 13:20
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Ty there was already one answer – Apr 03 '21 at 13:39
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The bottom line is that you can define whatever you like but it may be useless. The conventional definition of limits is useful. Yours is useless. – user21820 Apr 25 '21 at 08:01