First question here so please point me in the right direction if I'm doing this wrong.
The basic premise of my question is this : if we take any decimal number such as 0.02053 and "reflect" it about the decimal point the result is 35020.
It appears as if there are no decimals between 0 and 1 which cannot be manipulated in this way to give a unique result since even irrational numbers would simply create an infinitely large (but unique) number.
If we continue down this line of thought we can deduce that there is a 1:1 mapping between all decimals between 0 and 1 to all the integers.
I know this result is false but I'm unsure where my logic is slipping up.
Any answers are much appreciated :)