I was watching Veritasium’s video about math having a fatal flaw. He explained that if we make a set of all the numbers in between 0 and 1, then added one to the first digit of the first number and added one to the second digit of the second number etc, we would always have a new number. He said this proved that there were more numbers in between 0 and 1 than natural numbers.
I was confused as to why you can’t do this with natural numbers, and how that proved one infinity was smaller than another.
In: Mathematics
Same way an infinite one dimensional universe is just a dot to us. And an infinite two dimension is just a line stretching infinitely long, but wouldn’t take up all the space in our universe. And our infinite third dimension universe wouldn’t be able to completely fill up a forth dimension.
Infinity^0 is equivalent to 1. Not really big now is it
Infinity^2 is infinity*infinity.
Infinity^3 is comparable to the space our universe takes up
Time can also be considered a dimension, we experience time in one dimension, and time will never end so it is infinite. But we only experience it one moment at a time. Two dimensional time would be experiencing all that has happened and will happen at the same time, three dimensional time is all possible time lines from the starting point, or the creation of our universe. A zero dimensional time line would be like if you took a photo of the universe, a particular moment in time, and than nothing ever changes.
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