/sci/ - Science & Math

>>12501884

If you clarify for yourself what decimals actually mean, you will see that the distinctions you are making disappear, and that the "fundamental issue at hand" is not fundamental.

A.BCDE... means the real number

A + B/10 + C/100 + D/1000 + E/10000 + etc.

Here the infinite sum is defined as the limit of the sequence of numbers A ; A + B/10 ; A + B/10 + C/100 etc. which you can prove always exists.

In its decimal expansion, 1 is properly written as 1.00000... which really means

1 + 0/10 + 0/100 + 0/1000 + etc.

and you can show that this is the same as

0 + 9/10 + 9/100 + 9/1000 + 9/10000 + etc.

which is represented by the decimal 0.999...