Author Topic: Episode #736  (Read 2338 times)

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Offline jt512

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Re: Episode #736
« Reply #135 on: August 29, 2019, 10:41:32 PM »
I actually almost understood that! I'll need to re-read it a couple of times but thanks for the explanation.


It's, unfortunately, hard to avoid a degree of technicality.
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Offline arthwollipot

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Re: Episode #736
« Reply #136 on: August 29, 2019, 10:45:29 PM »
I actually almost understood that! I'll need to re-read it a couple of times but thanks for the explanation.


It's, unfortunately, hard to avoid a degree of technicality.

My job in IT partially consists of getting non-technical people to understand technical issues, so I totally get it. I'll muddle along as best I can.  ;D
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Offline stands2reason

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Re: Episode #736
« Reply #137 on: August 30, 2019, 10:39:24 AM »
One distinction is that rational numbers are countably infinite. But irrational numbers are uncountably infinite. They have the same infinite density in every numerical range, is one way to think of it. An irrational number is represented mathematically as an infinite string of numbers. Since it is irrational, it does not have an exact representation in any number system, so it would take an infinite sequence of digits to exactly describe it. This is a distinction from rational numbers, where we know that 0.3... is exactly 1/3, and so on. If a number doesn't have an exact representation, it repeats. Irrational numbers do not, by definition.

Take that infinite set of irrational numbers in the [0,1) and multiply it by 0.1 (just for the convenience, of thinking of the string of digits, in decimal). Now, you have that same infinity in [0,0.1). And add 0.1 offsets, you have that same infinity in the range of [0.1, 0.2), [0.2, 0.3). Now, the use of decimal is arbitrary, the same idea applies for any scalar or number base system.
« Last Edit: August 30, 2019, 12:31:00 PM by stands2reason »

Online brilligtove

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Re: Episode #736
« Reply #138 on: August 30, 2019, 11:57:17 AM »
This Numberphile video has a basic intro to some of the ideas that make infinity so weird.



There are lots of other videos out there, of course.
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Offline stands2reason

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Re: Episode #736
« Reply #139 on: August 30, 2019, 12:38:39 PM »
Actually, I got it wrong that I described countable infinity as having different sizes. Mathematically, there is actually no such thing as countable infinities having different sizes. I see the Numberphile video explains exactly this, as well as irrationals.
« Last Edit: August 30, 2019, 12:47:36 PM by stands2reason »

Offline arthwollipot

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Re: Episode #736
« Reply #140 on: September 01, 2019, 09:36:00 PM »
I know a little bit about Cantor, and I've saved that video to watch later. Numberphile is already in my subscriptions, as is standupmaths.
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Online brilligtove

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Re: Episode #736
« Reply #141 on: September 02, 2019, 12:23:28 PM »
I know a little bit about Cantor, and I've saved that video to watch later. Numberphile is already in my subscriptions, as is standupmaths.
I checked Matt's feed for a video on infinities first. :)
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