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PeroK replied to the thread High School Why does continuity still feel weird?.That isn't the idea at all. The idea is that you can use the theorems about sequences that you will already have developed in your... -
PeroK reacted to mathwonk's post in the thread High School Why does continuity still feel weird? with
Sad.
In fact, when stated precisely, the sequential version is even more complicated, i.e. it is being abbreviated above by the unexplained... -
Welcome to PF. Is the context of your question relativity theory? If so the answer is that "now" is well-defined for you at your own...
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PeroK reacted to RicoGerogi's post in the thread High School Why does continuity still feel weird? with
Like.
That epsilon-delta negation is definitely clumsy, a single sequence feels much cleaner -
PeroK replied to the thread High School Why does continuity still feel weird?.It depends. Generally, it's not any easier for proving a function is continuous - because you have to consider every possible sequence...
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PeroK replied to the thread High School Why does continuity still feel weird?.If you have to sit a standard analysis exam, then appealing to hyperreal numbers won't help.
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PeroK replied to the thread High School Why does continuity still feel weird?.An alternative, which is equivalent to the usual epsilon-delta definition is: A function ##f## is continuous at a point ##a## if for...