I apologize if this question is in the wrong forum, I am not a math student and have no clue which branch of mathematics this question would fall under. In fact my profound ignorance of math makes it so I don't even know if this is a stupid question till I ask it. Since most problems that nag at me in insomniac moments are not number related, I can easily track down more information if I can't figure the answer out myself, but here I have had no luck with Google or any of the basic explanations of series and sets I've found online, so even a few search terms to help put me on the right track in lieu of an answer would be helpful.
If I remember right the series of natural numbers 1,2,3,4... is an infinite series, and the series of negative numbers -1,-2,-3,-4... is an equally infinite series. But doesn't this make zero the midpoint of a series that runs into infinity on both ends? This feels paradoxical to me since I thought it was impossible to calculate a midpoint to infinity.
So anyway, I assume I must be making an error in my premise (searching so far indicates possibly by misunderstanding the definition of the word "infinite" as it used in math in general or with number series specifically?) but I don't know exactly and am stuck in trying to track it down. Again,sorry if this is an idiotic question but for whatever reason it's nagged at me for a day or two and I figured I'd take a shot and see if anyone here could explain it to me or set me on the right scent to find out more on my own.
infinte things don't behave like finite things. it's apples and oranges. half of a finite thing is less than the original thing. half of an infinite thing...still infinite. you can even chop up infinity infintely many times....and STILL have infinity:
1) we'll put all the even numbers in this bag.
2) we'll put all the odd multiples of 3 in this bag.
3) put all the odd multiples of 5 that aren't multiples of 15 in this bag.
4) odd multiples of 7 that aren't multiples of 21 or 35 in this bag.
we'll wind up with an infinite number of bags (one for each prime), and each one will have an infinite number of integers in it. try doing THAT with a finite number....
Thanks so much!! I have always had trouble with math I can't put into context by imagining it spatially, strangely enough. I was an English major who failed college algebra twice, and had no hope of passing until I found a kind professor who didn't think I was pulling his leg when I begged him to arrange that all my tests be mainly in the form of word problems, which would allow me to solve the exact same problems that when just presented to me as equations might as well have been cuneiform as far as my ability to decipher them. I don't know what that particular mental block would be called, Math dyslexia? And no matter how much I meditate I have never been able to conjure up a nice image of infinity to rotate like I can a geometric shape
Since my last Math class was over 20 years ago, compound ignorance with atrophy -- aside from finding some lovely reading on zero and infinity, until I figured it'd be best to risk asking a stupid question here than just give up, I couldn't even come up with concise enough searches to yield anything beyond that same simple and symmetrical grade school number line I had in my head and was messing me up. You all were super helpful right off in giving me the simplest answer and even better, with your comments as a springboard for inquiry, I have spent the evening happily refreshing myself on real and imaginary numbers, infinite sequences and sets, and reading all about the Cauchy sequence and Topological spaces (which I don't understand at all yet!).
Thanks again for helping a math moron with a curious mind and pointing me in a more fruitful direction, ( And the icing is that 5 hours of reading about math appears to be a cure for insomnia--my brain is fried and so Good Night to you)!!