Astronomy Cast Ep. 267
"Infinities"
The episode starts out by defining what infinity really is, with an example about counting grains of sand on a beach. While it is possible because there is a finite number of grains, it is still impossible for one person to do because the number is so large. However there are things that are impossible to count, not because they are so large, but because they are not finite numbers. It then transitions into explaining that there's more than one kind of infinity! Some are smaller, some are larger, but there is no one infinity!
Infinite numbers exist right under our noses too, take for example all the numbers between 1 and 2...1.1,1.11,1.01...2 In truth, if you kept adding decimals, you could keep going forever!
We've discovered that the universe is still expanding, and is almost flat. So in the end, we don't know if it is infinite or not, but it is almost certainly infinite...just really really big...Kind of like how the Earth was seen in the 18th century. This all just blows my mind! There's so much to even simple numbers that we have yet to fully understand!
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