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Yeah, very surprising, as they are otherwise really good at separations.Ibix said:
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dkotschessaa
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Used my beard trimmer before coming to work today. When I looked in the mirror at work there was one grey one that apparently survived the trimming. Tried to pull it out by hand, but the tough lil' bastard will not leave.
I'm actually encouraged by this, as I am sure it is some kind of metaphor for ageing.
-Dave K
I'm actually encouraged by this, as I am sure it is some kind of metaphor for ageing.
-Dave K
Enigman
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The old that is strong does not wither,dkotschessaa said:
Deep roots are not reached by the frost.
dkotschessaa
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People from the Philippines are Filipino, not Philipino, and I find that conphusing.
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How do you call people from Illinois?
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fresh_42 said:
Hmm ...
...i remember one called an "Illini Eyefull" .
http://www.explayboybunnies.com/biographies/diannechandler/dianne.html
OmCheeto
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Not sure what the people are called, but I seem to recall a conversation from about 35 years ago where someone from Missouri referred to Illinois as; "Illinoise", and vice versa; "Misery".fresh_42 said:
hmmmm... I wonder how French people pronounce "Illinois"?
Il-lay-nwah? Ee-lee-nwah?
Never bin to France. I have a new Facebook girlfriend from there though. She seems nice. Though... hmmmm... I think she's 1/3 my age, so I think I put her on FB "mute" about a month ago. Young people's brains work to fast, IMHO.
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I thought it might have been something noisy.OmCheeto said:
But "Misery" is good one.Should be no problem: Illinoises doesn't sound noisy in French. But I'm not sure whether it's French at all. They have a lot of indigenous names up there.
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Sounds annoying.nuuskur said:
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Enigman
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With my phone.fresh_42 said:
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People come to me after seeing a youtube video about how the sum of all natural numbers is some magical [itex]-\frac{1}{12}[/itex] and they back it up by saying " .. but they say it's often used in QM, so it must be true..!" . I'm like: nope, that is not the sum of natural numbers :(
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It is in a certain sense when involving analytic continuation of a function* that produces that sum. https://en.wikipedia.org/wiki/1_+_2_+_3_+_4_+_⋯nuuskur said:
*(for example the Riemann Zeta function of -1.)
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I have seen a few proofs of the claim. One that abuses the Riemann zeta function [itex]\zeta (s) := \sum_{k=1}^\infty \frac{1}{k^s}[/itex]. This is valid only when [itex]Re(s)>1[/itex]. and they conclude result by
[tex] \zeta (s) = 2^s \pi ^{s-1}\sin\left (\frac{s\pi}{2}\right )\Gamma (1-s)\zeta (1-s)\vert _{s=-1} = -\frac{1}{12}[/tex] which, indeed, is true, but its association to the series representation is invalid. Then there is the geometric series "proof" where they say [itex]\sum_{k=0}^\infty x^k = \frac{1}{1-x}[/itex] and they do mention that it is valid when [itex]x<1[/itex], but then conviniently set [itex]x=-1[/itex] and conclude their result. In reality, the sum is valid when [itex]|x|<1[/itex] i.e they cheated. It's known as ex falso quodlibet. Proceed under false assumptions and conclude that the Sun is smaller than the Earth.. hooray. Not quite -.-
If we involve analytic continuation then we are no longer talking about the sum in the traditional sense. This is the part people get confused, because nobody explicitly states that we aren't actually talking about the sum in the sense of addition. It's more like, we assign a value to this series and prove that the operation is valid. But that's not exciting, is it?
I wouldn't be studying pure mathematics if the principles of logic were so easily defied without consequence. The heretics may preach what they wish, at that point, what they dabble in is no longer backed by logic, therefore not mathematics.
[tex] \zeta (s) = 2^s \pi ^{s-1}\sin\left (\frac{s\pi}{2}\right )\Gamma (1-s)\zeta (1-s)\vert _{s=-1} = -\frac{1}{12}[/tex] which, indeed, is true, but its association to the series representation is invalid. Then there is the geometric series "proof" where they say [itex]\sum_{k=0}^\infty x^k = \frac{1}{1-x}[/itex] and they do mention that it is valid when [itex]x<1[/itex], but then conviniently set [itex]x=-1[/itex] and conclude their result. In reality, the sum is valid when [itex]|x|<1[/itex] i.e they cheated. It's known as ex falso quodlibet. Proceed under false assumptions and conclude that the Sun is smaller than the Earth.. hooray. Not quite -.-
If we involve analytic continuation then we are no longer talking about the sum in the traditional sense. This is the part people get confused, because nobody explicitly states that we aren't actually talking about the sum in the sense of addition. It's more like, we assign a value to this series and prove that the operation is valid. But that's not exciting, is it?
I wouldn't be studying pure mathematics if the principles of logic were so easily defied without consequence. The heretics may preach what they wish, at that point, what they dabble in is no longer backed by logic, therefore not mathematics.
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dkotschessaa
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jim hardy said:
That is actually a very well crafted and quoteworthy statement.
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DennisN
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DennisN
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Science in ancient Egypt: hierophysics.
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Easily said. Since I've heard Iggy in a commercial, I mean Iggy, ... I've lost all my trust in this world.WWGD said:
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Yep. Not himself, just his song.
... half naked old men don't sell well even here ...
... half naked old men don't sell well even here ...
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The new year just started in Iran. We entered 1396!
I hope tensions start to decrease all over the world.
I hope tensions start to decrease all over the world.
dkotschessaa
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WWGD said:
Dreading the arrival of summer here in FL. "Winter" has been beautiful. Even spring has been kind of mild with a few days in the upper 80s.
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Mom says, I'm still a planet!
zoobyshoe
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I watched a video of a small house being printed by a large 3-D printer. Instead of plastic it was "printing" in cement. That pushed me over into now believing that 3-D printing is the future of everything.
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Dang, I just recognized, that I know what a choke is.