Braininvat » July 23rd, 2018, 12:00 am wrote:
To keep this on topic I will note that the surface of a wax cylinder is, in one sense, infinite.
Gosh, that was clever.
Tee hee :-)
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Braininvat » July 23rd, 2018, 12:00 am wrote:
To keep this on topic I will note that the surface of a wax cylinder is, in one sense, infinite.
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Most people would assume that that if you define a set of numbers (such as integers running forwards to infinity), then it is full populated because you haven't included any limitation in your definition.
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phyti » August 28th, 2018, 11:57 am wrote:The limitation is: 'the set cannot end'! Thus cannot be made manifest, thus no proof it exists.
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phyti » August 30th, 2018, 12:37 pm wrote:That is what I meant, per the dictionary definition.
Any 'contructivist' method of an infinite list, could never be complete.
The mind can only comprehend a complete list (a finite entity) by identifying boundaries, a beginning and an end.
Time is also relevant to the method, when would it be complete?
Any Peano type method allows the formation of larger integers, but not the largest integer.
I.e., you can only extend a list.
Infinite llterally means 'without end', so an 'infinite list' is actually a contradiction of terms.
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ronjanec » August 30th, 2018, 2:05 pm wrote:I personally define ‘infinity/infinite’, as the particular way in which someone or something is said to have absolutely no end or possible limit to the same.
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Brent696 » August 30th, 2018, 2:28 pm wrote:
BTW, I believe SP is out of town for a few days so it might be a while before he gets back to his thread.
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someguy1 » Thu Aug 30, 2018 2:33 pm wrote:ronjanec » August 30th, 2018, 2:05 pm wrote:I personally define ‘infinity/infinite’, as the particular way in which someone or something is said to have absolutely no end or possible limit to the same.
Isn't the set of real numbers between 0 and 1 inclusive, an infinite set? And aren't 0 and 1 the ends? And aren't they limit points of the set? In fact isn't every point of the closed unit interval a limit point?
Reason I mention this is that math has a well-developed theory of infinity, 144 years old at this point. You're not entirely entitled to make up your own without supplying justification, background, and context. We don't believe in the phlogiston theory of heat anymore. Science and knowledge move forward.
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someguy1 » August 30th, 2018, 4:34 pm
He went someplace where there's no internet? When I go out of town the first thing I do when I get to my destination is get connected to motel internet. How about you?
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Brent696 » August 30th, 2018, 3:40 pm wrote:
He just told me he would be incommunicado for a few days.
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DragonFly » August 30th, 2018, 5:24 pm wrote:We can let the fractions between 0 and 1 be potentially infinite, for math purposes, but we cannot list them all.
DragonFly » August 30th, 2018, 5:24 pm wrote:Plus, we can call convergences to 1 in math to have gotten to 1.
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Braininvat » August 30th, 2018, 6:15 pm wrote:SG, Want to be a moderator? I'm tired.
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someguy1 » August 30th, 2018, 6:36 pm wrote:The rationals are easily listed. Here's a visual proof intended for high school students. Surely most here have made it through high school.
someguy1 » August 30th, 2018, 6:36 pm wrote:That doesn't parse. What do you mean?
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Brent696 » August 30th, 2018, 7:52 pm wrote:I found the bold lettering and smiley face extremely disturbing and unprofessional on a tutorial.
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Brent696 » August 30th, 2018, 11:15 pm wrote:Are we distinguishing between within the dimensions of time and space? I find no infinite within the universe but a certain one transcendent to it.
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Brent696 » August 31st, 2018, 10:51 am wrote:Science stops at the door of the universe, that which is finite, it utilized "potential" infinities in conceptual ways but the universe does not allow for any actual infinities.
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davidm » August 31st, 2018, 1:18 pm
Had this discussion before. It is possible that the universe is infinite in space and time. Since this is possible, it is wrong to say that that the universe does not allow for actual infinities.
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