It can't be disproved, 1 is just equal to 0.9999999.

Method 1: We know that 1/3 is equal to 0.33333...2/3 is equal to 0.66666..., so 1/3 + 2/3 must equal 0.3333 ...+0.6666....

The two sides are added together, resulting in 1 = 0.999.......

Method 2: Given a set of sets of intervals, there is exactly one point on the number axis that is contained in all those intervals; 0.999... corresponds to the interval sets [0, 1], [0.9, 1], [0.99, 1], [0.999, 1] ... , and the only intersection of all these intervals is 1, so 0.999... = 1.

Method 3: All rational numbers smaller than 0.999... All rational numbers smaller than 0.999... are smaller than 1, and it can be shown that all rational numbers smaller than 1 will always be different from 0.999... somewhere after the decimal point (and thus smaller than 0.999...). (and therefore less than 0.999...), which means that 0.999... ), which means that the Dedekind partition of 0.999... and the Dedekind partition of 1 are exactly the same set, thus showing that 0.999... = 1.

Cyclic number property:

Multiplying by a prime number that produces a cyclic number results in a series of 9s. e.g. 142857 × 7 = 999999.

If it is divided bit-wise into a number of equal-length portions and added, the result is a series of 9s.This is a special case of Midy's theorem. case. For example 14 + 28 + 57 = 99 142 + 857 = 999 1428 + 5714+ 2857 = 9999. all cyclic numbers are multiples of 9.