/sci/ - Science & Math

A friend told me he had seen his physics teacher prove that
1+1+1+...+1 (infinity time) equals -0.5.
WTF? Is it possible? Sounds like trolling, but I have to know.

Wikipedia is a reliable source of information.

Source:http://en.wikipedia.org/wiki/Reliability_of_Wikipedia

Hey /sci/,

A God here (there are many of us), here is the answer to everything. Consider homo-sapien science fix'd.

You're welcome.

OK /sci/ serious question time.

We all know that .999...999 (that is to say an infinite chain of nines after a dot)=1

This is easily proven because
1/3=.3333...333
2/3=.666...666
3/3=.999...999
3/3=1

Therefore .999...999=1

My question, and this isn't a troll thread, I want to know, how to mathematicians handle this? I mean we round in math all the time, but its for physics or applied stuff, so an infinitely small number doesn't matter. However, in theoretical math of course an infinitely small number matters, if it didn't then why can't we just say, oh well if one of these numbers doesn't matter than no small number really matters, why are we spending so much time computing pi when its inifinith digit doesn't even matter? How far down do you have to go before math just says "fuck it"?

Further, if .0000...00001 is ok to ignore, than shy not ten tomes that number? or ten times that one? or infinity times that one? How can math stand on its own when its all theoretical but its basically saying no number matters?

I got in an argument today with my Algebra II teacher. She shown us a graph modeled after a cubic polynomial equation and she said "The line continues on, closer and closer to infinity."

To which I inquired, "How can something be closer to infinity? If Infinity is always larger, no matter what number you have in mind, wouldn't, say, 5 and 0 be the same distance?"

She disagreed, as did the rest of my class. Although, I think the students were a victim of argument from authority. Who is correct? Myself or my teacher?

Is viewing things ( meaning anything in any shape or form) as fragments of infinity, be it infinity in time and space) a good or bad way to look at things(same meaning as above)?