So I had a thought today... if most numbers exist transcendentally, meaning that their decimal expansion exists infinitely and does not repeat or have patterns, then are there even more numbers out there that are infinitely bigger with infinitely bigger bases since there are an infinite number of infinities (cantor)? What I am saying is that there is theoretically no limit to any number in its bigness or its smallness, so in effect there are more Super Big numbers than Super Small numbers even if they are transcendental in nature?
For example if you had the number 0.10923523421... etc. and it continued on forever, but then added one, it would then be 1.10923523421... In fact you could keep adding the next higher base that reflected its inverse base (tens to the tenths, hundreds to the hundredths, etc...) so it would look like ...12432532901.10923523421... (where the preceding ellipses implies that it goes on beyond the highest base indicated)
If this is true then does that mean that infinity is actually a base and that base infinity in decimal would just be 1x10^?, and that you could have multiples of this and even work in base infinity algebraically? Like you could add two infinities together to be 1x10^?+1x10^?=2x10^??
For example if you had the number 0.10923523421... etc. and it continued on forever, but then added one, it would then be 1.10923523421... In fact you could keep adding the next higher base that reflected its inverse base (tens to the tenths, hundreds to the hundredths, etc...) so it would look like ...12432532901.10923523421... (where the preceding ellipses implies that it goes on beyond the highest base indicated)
If this is true then does that mean that infinity is actually a base and that base infinity in decimal would just be 1x10^?, and that you could have multiples of this and even work in base infinity algebraically? Like you could add two infinities together to be 1x10^?+1x10^?=2x10^??
