Magnus Anderson wrote:Ecmandu wrote:1/9 = 0.111...

Your word “are” also means “equals” in my case above, a finite expression “is” (are) equals an infinite expression.

The way I understand it, what you're saying is:

1) \(0.111\dotso\) is an infinite sequence.

(Disagree.)

2) \(\frac{1}{9}\) is a finite sequence.

(Disagree.)

3) \(0.111\dotso = \frac{1}{9}\) is true.

(Disagree.)

4) If #1, #2 and #3 are true, it follows that there is at least one infinite sequence that is a finite sequence.

(I'm inclined to agree with this.)

The problem is that \(\frac{1}{9}\) and \(0.111\dotso\) are not sequences. They are numbers. (And it's also not true that \(0.111\dotso = \frac{1}{9}\) but that's a peripheral issue.)

Ok, we’re going to dig at each other every so often, so I’ll just ignore your post after this.

So...

I found it interesting that you omitted the sequence:

1/10+1/100+1/1000+1/10000 etc...

But just decided to write 0.111...

The first part IMPLIES the sequence!

1/9 is finite in that it is a rational in its fraction form!!

0.111... is a repeating rational in its decimal form.

All of this shit:

1/9

0.111...

1/10+1/1000*1/1000 etc...

All equal each other!

I have no clue why you are playing such subtle word games that don’t change the content of what I wrote whatsoever, but here you are, doing just that!