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86tuning t1_iuadijl wrote

infinity is not a number, it's an idea. so you can't have infinity plus one, or infinity divided by two.

if you count 1, 2, 3... and never stop, you'd never get to the end, because the series is infinite.

the kicker is that some infinities are bigger than others. consider the set of positive whole numbers or integers above. there's an infinite number of positive whole numbers. but there's also an infinite number of even numbers, and an infinte number of odd numbers. and the infinite number of whole numbers is clearly bigger than even or odd ones.

fun times, right?

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timhamlin t1_iuaf7ze wrote

Another perspective on infinity is the coastline problem. If u measure a coastline you have to define the resolution of the map. If it’s in inches, rather than miles or yards it will result in a MUCH greater number for the same section of coastline. If u increase the resolution to infinity, you make the measure of the coastline infinite. There is an infinity in every minute dot.

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DavidRFZ t1_iuapi30 wrote

Yeah, you can paint an infinite area with a finite amount of paint.

The area under the curve 1/x from 1 to infinity… infinite.

The volume of the curve 1/x from 1 to infinity revolved around x-axis… finite!

The area clearly fits inside the volume!

But then you need to consider practical issues like the size of the atoms and molecules that make up the paint.

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blow_up_the_outside t1_iuarx9a wrote

You can for sure have infinite numbers plus one, or divided by two.

Those kind of numbers are called transfinite numbers (ω, ℵₒ, m)

They are not finite, just not absolutely infinite (∞).

But a transfinite number t + 1 is, well, (t + 1) and t / 2 is (t / 2)

Which is not the case for ∞ + 1 or ∞ / 2 which both are still ∞

Maybe I shouldn't go into transfinite numbers in eli5...

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