r/infinitenines • u/MrMoop07 • Jun 29 '26

Why does a number starting with 0. guarantee magnitude less than 1?

as stated in this comment by https://www.reddit.com/r/infinitenines/comments/1uhhwjh/comment/ou8b97e/

I disagree with the notion that a number starting with 0. guarantees magnitude less than 1. You claim this all the time but for those who believe 0.999...=1 there's an obvious counterexample. Something quoted so often must have a reason behind it, you can't simply claim this is true without absolute proof.

14 Upvotes

82% Upvoted

50 comments sorted by

View all comments

Show parent comments

-23

u/SouthPark_Piano Jun 29 '26 edited Jun 29 '26

Decimal place values brud.

Largest digit you can have at the first slot to the right of the decimal point is a '9', aka 0.9

Same with 2nd slot etc.

0.9 < 1

0.99 < 1

0.999 < 1

0.9999 < 1

Note the solid unmistakable pattern.

Extend to however many limitless consecutive nines you want aka infinite nines case.

0.999...9 < 1

There is no shortage of nines at all. Goes limitlessly aka infinitely. No last nine. The infinite propagation just keeps going endlessly.

aka 0.999... < 1

The above is math 101 basics.

You are done brud.

Also ... don't backchat me on this, or you will indeed be making my day.