u/Calm_Improvement1160

And for the ones you don't agree with, would you agree that they are equal to 1?

1. The number with the property that for all natural n ≠ 0, the nth digit past the decimal point is 9
2. lim x →∞ 1 - 10^x
3. lim x →∞ sum from n= to x (9/10^n)
4. 1/3 * 3 = 0.333... * 3 = 0.999...

Edit: Fixed 3

If we were to define a relation D(a,n) which give you the value of the number a at the nth decimal place, for which singular n would D(0.00...1, n) = 1, or rather, for which n does D(0.00...1, n) ≠ 0

SPP tells us that the number 0.(9) is embedded in the set {0.9, 0.99, 0.999, ...} but what does that mean?

Can every number be embedded into a set?

What number is embedded into the set {0.99, 0.999, ...}?

How do you tell, from 2 given sets, whether the numbers they embedd are equal?