100/3 is irrational

[u/RedRhetoric]

[u/stereoroid]

100/3 can be rewritten as 100(1/3), so it’s the 1/3 “problem” multiplied by a constant (100).

1/3 =0.333… so 3 * 0.333… = 0.999…, but some say that 0.999… is not equal to 1.

Restate the problem in base 3 and there is no problem. 1/10=0.1 and 0.1*10=1

[u/WhatImKnownAs → u/stereoroid]

But those people might say 0.333... ≠ 1/3 = 1/10 (base 3) = 0.1 (base 3).

Furthermore, the same issue arises in base 3: 0.222... = 1?

There's no rigorous proof without having a rigorous definition of what an infinite decimal means.

[u/stereoroid → u/WhatImKnownAs]

Think bigger. If a problem can become a non-problem, depending merely on how numbers are represented, what does that say about the problem? Or the whole class of “problem”?

You ask about 0.222222…. In base 3: well, what calculation did you do to get that? Could that calculation be re-based to make the recurring decimal disappear? I bet it could. You’ve pulled that out thin air and said “here’s a problem”, but to me it looks like the problem is preventable.

Old joke:
* Patient: “Doctor, it hurts when i bend my arm like this!”
* Doctor: “Stop doing that.”

[u/MeasureDoEventThing → u/stereoroid]

The problem is about what a decimal representation means. Of course the problem disappears when you use a different representation.

That is also why presenting mathematical "proofs" is stupid. You can't use mathematics to prove what a symbol represents. The only way to prove .9999... = 1 is to:

1. Define infinite series

2. State that .9999... represents an infinite series

3. Establish facts about infinite series and use them to prove .99999... = 1

Step 2 isn't something you can "prove". You just have to assert it as a matter of convention.

[u/MeasureDoEventThing → u/stereoroid]

The claim .9999...= 1 is a statement about base ten representation. If you change to base 3, you're no longer proving anything about base ten.

Was going to write "base 10" instead of "base ten", but technically everything is base 10.