oh, i didnt realize i distance from A to B of 1 was infinite...
my bad, you are just plain smarter than me I guess....



Yeah, I guess one of the historical paradoxes that lead to the ideas of convergence would be irrelevant in proving 0.999... converges to 1 huh

edit : +21

This post was edited by Taxidermy on May 7 2010 04:50pm

Am I wrong? I just recently had a discussion with some pretty high-level math nerds who pointed out that wasn't a thing. You can't say .999...1 because there's no end to tack that one on. The ... means there is literally no end whatsoever.

Feel free to show me a source that says you can put something at the very end of infinity, but until then I'm more inclined to believe people with real credentials.

yep you could only say something like

0.999...1...

so theres a 1 in there somewhere but you cant say its at the end thats impossible

edit : +22

This post was edited by Taxidermy on May 7 2010 05:11pm

I am pretty confident infinitesimals exist.

sure but you'd have to define it more carefully

usually its called epsilon and you say its less than something

edit : +23

This post was edited by Taxidermy on May 7 2010 05:26pm

Okay, I'll admit that coming up against the edge of my knowledge and not knowing about hyperreal numbers tripped me up. But what I'm saying is still true if you're talking about real numbers.

Only as ghosts of departed quantities.

wait no!? This doesn't make sense....

kinda but then not really

It's a famous quote making fun of infinitesimals. They don't exist in traditional analysis and cannot be well-defined as real numbers. Non-standard analysis treats them, but that's not something anyone serious really cares about anymore.

Mods should really lock this thread about now. It has served its purpose.