I'm thinking Greta is a she but of course handles are arbitrary self-selected labels.marsh8472 wrote: I've understood everything you've said. I think he's just saying it's interesting. Within real numbers and with limits 0.9999... = 1. But on another level is 0.9999...=1 true too? Using criteria like these https://en.wikipedia.org/wiki/Criteria_of_truth

I have actually been thinking that this is the best .999... convo I've ever been in. They usually devolve terribly.

I hope I misunderstood that post in fact.

Anyway you are two or three posts ahead of me at this point but you've said some very interesting things I'd like to respond to in the next day or so. One thing I did want to say to you is that when you said you're an applied mathematician, I cracked up laughing. You are

*exactly*the person I'm talking about I hope you understand my sense of humor about that. You raised several specific mathematical points that I'll try my best to address. There's nothing circular about the definition of the real numbers and the definition of an infinite sum. In fact they do that in calculus class. The sum of an infinite series is the limit of the sequence of partial sums. That's actually a clever trick. There really is no such thing as an infinite sum 9/10 + 9/100 + 9/1000 + ... Rather, that notation is defined as the limit of the SEQUENCE 9/10, 99/100, 999/1000, ... and you yourself provided the definition that the limit is 1.

But this is another good example of how in math we finesse things but forget to explain it to the general public. There is no such thing as an infinite sum of real numbers. The sum itself is simply defined as the limit of the sequence of partial sums. And sequences are kind of more believable than series, don't you think? People wonder, What does it mean to add up infinitely many real numbers? And the answer in math is that we

*never actually do that*. Instead we redefine the sum as a sequence, and we define limits of sequence in terms of epsilon and N and a couple of quantifiers. We never actually added infinitely many real numbers at all! Does that make sense?

I do agree I might be a little obsessed with this topic. About two years ago I promised myself never to engage in another .999... thread online. A year ago I broke my rule, spent a few weeks arguing with a crank, and regretted every minute of it.

This is the best .999... thread I've ever been in. I'm getting to articulate a lot of things that are on my mind about this subject. I can see how it all seems a little over the top.