mathwonk's latest activity
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Mmathwonk reacted to Matterwave's post in the thread Hi! Can someone explain about Differential Equations? with
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You already solved the differential equation here so it might be hard to tell what it was. The differential equation originates from... -
Mmathwonk reacted to RicoGerogi's post in the thread High School Why does continuity still feel weird? with Like.
f is clearly not continuous at 0 (sequential def makes it obvious with any sequence xₙ→0) but it's continuous everywhere else since...
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Mmathwonk replied to the thread High School Why does continuity still feel weird?.@PeroK: I like your suggestion to use previously proved general theorems to deduce discontinuity of specific functions. One such...
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Mmathwonk replied to the thread High School Why does continuity still feel weird?.I apologize for provoking sad faces by post #12. To be honest, most people will not need to give an actual proof of sequential...
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Mmathwonk replied to the thread High School Why does continuity still feel weird?.midget dwarf, nice example, but there is a typo in your statement; likely you meant f(0) = 1, but f(x) = 0 for x ≠ 0.
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Mmathwonk reacted to MidgetDwarf's post in the thread High School Why does continuity still feel weird? with Like.
Rule of thumb: If you want to prove that something is continuous, use Epsilon delta definition of limit. If you want to disprove...
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Mmathwonk replied to the thread High School Why does continuity still feel weird?.In fact, when stated precisely, the sequential version is even more complicated, i.e. it is being abbreviated above by the unexplained...
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Mmathwonk replied to the thread High School Why does continuity still feel weird?.A little symbolic logic notation is useful for easily negating basically anything. I.e. to negate, you exchange the type (universal vs...
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Mmathwonk reacted to jedishrfu's post in the thread High School Why does continuity still feel weird? with Like.
No but hyperreals could offer a check on your answer which I realize is a poor second to, getting the epsilon-delta proof correct in an...
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Mmathwonk reacted to PeroK's post in the thread High School Why does continuity still feel weird? with Like.
An alternative, which is equivalent to the usual epsilon-delta definition is: A function ##f## is continuous at a point ##a## if for...
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Mmathwonk replied to the thread Hi! Can someone explain about Differential Equations?.watching the movie Ivanhoe today I was interested in the height of the famous fall off the castle by the great stuntman Paddy Ryan...
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Mmathwonk replied to the thread Undergrad What is "x" in this definition of a basis?.I think your new book is probably a good choice.
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Mmathwonk replied to the thread Undergrad What is "x" in this definition of a basis?.yes they meant what you said. however this is a strange definition, as property 3 follows from property 2, so is not needed. The book...
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Mmathwonk replied to the thread Undergrad The natural numbers and logical consequences of them.the fact that the natural numbers contain an infinite number of disjoint infinite subsets, implies for the arithmetic of infinite...