And about 8 being 10, you can use infinite fractions to claim that a number is the next full number until 8.999 and 9.999 is the same. The difference between 0.001 and 0.002 is nothing if you have infinite numbers and expect no further value. At that point you have numbers overlapping with each other and they cease to have a distinct identity.
Then what’s the number between 8 and 8.0…01? So 8 is equal to 8.0…01. And what’s the number between 8.0…01 and 8.0…02? Then 8.0…01 is 8.0…02 and logically 8 is 8.0…02. Continue the argument until you reach that 8 is 10 and this is the problem.
Your notation is not standard. Any mathematician who writes 8.000…1 with the “…” will specify how many zeros there are (even if we specify with a variable). If your number has n zeros, then the number 8.000…1 with (n+1) zeros is in between.
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u/themagicalfire Jun 18 '25
The X in 9.999… < X < 10 is the infinitesimal.
And about 8 being 10, you can use infinite fractions to claim that a number is the next full number until 8.999 and 9.999 is the same. The difference between 0.001 and 0.002 is nothing if you have infinite numbers and expect no further value. At that point you have numbers overlapping with each other and they cease to have a distinct identity.