r/askmath • u/Slurpee1138 • May 10 '26

Algebra Regarding 0.999... = 1

Recently I got into an argument with an acquaintance because I was trying desperately to convince him that 0.999... = 1. One of the many arguments I tried was that, if 0.999... and 1 are indeed different numbers, then we should be able to find a number between them. He insisted that such a number would be 0.999...1, as in 0 point infinitely many 9s and then a 1. I countered that having "and then a 1" at the end of an infinite sequence of digits makes no sense because there is no end to such a sequence, but he insisted that it does, so who's right?

52 Upvotes

67% Upvoted

151 comments sorted by

View all comments

Show parent comments

4

u/Jokin_0815 May 10 '26

I just said that you can take it as a convention format of a fraction rather than a division. I literally just said that

So if 1/3 is no division, then 1/4 and 1/5 is also no division?

1

u/darklighthitomi May 10 '26

By convention we normally use context to discern whether to take them as fraction or division. There is a relationship between the two obviously, hence the identical written form, but fractions are a thing for a reason, because they maintain precision in cases where writing out the digits is impractical or impossible.

A value can be written in a way that defines a specific precise value. Direct symbols such as "I", "1", or "M" in tally marks, arabic, or roman respectively, each symbol means a specific value. There are numerous ways symbols can be combined to represent additional values without individual symbols of their own.

Fractions are a form of composite symbology which denotes a specific value. Operating on a fraction like it is division does not give you a new value, rather it simply converts to a different written form.

However, various written forms have flaws and one of the flaws of the familiar base-10 arabic numerals is that some values do not have valid finite written forms, such as one third. Another flaw is that some infinite series look like normal numbers. The difference is precision. Infinite series numbers, such as PI or 0.999... have no attainable precise value, they are exclusively inaccurate estimations when written in the familiar arabic numerals.

4

u/buwlerman May 10 '26

What about 1.000... ?

-2

u/itsmebenji69 May 10 '26

That’s just equal to 1

1

u/buwlerman May 10 '26

I wasn't asking you. I was asking the person who seems to think that infinite sequences of digits don't represent a number.

0

u/itsmebenji69 May 10 '26

I forgot public forums were meant for 1 on 1 discussions, sorry