I alway found this a interesting topic, even though I not good at most math. Let's supose that you have group of lines making a triangle (sort of) like this:
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Now if it keep go (ignoring for a minute the fact that atom are the smallest unit of matter) the top lines will continue forever. The triangle though must remain equal on all sides. So, now we have Infinty in a finte space!
I am sorry the triangle didn't come out the way I wanted, but it still works.
Why would it be a finite space?
I hate how NTs always say that you can't imagine infinity. Finity proves infinity- it's infinitely finite. I love that. For anything to be solid, it has to be infinitely present. The idea of forever, infinite time- it fills me with glee.
I love the concept of infinity. You can imagine it by its very nature you can't see it (our brains are only finite after all). When I think about it very, very deeply, it's like this little window opens and I can feel and see all existance, but only for a second, it's like having a mild electric shock.
I probably sound crazy, but I can't think of any better way to describe it. If I can, I'll be back!
If you keep on adding lines, you'll still have a finite amount of lines there. It would take an infinite amount of time to add enough lines for it to become infinite, but you would still have a finite shape with a finite amount of space in it. Your theory is that we can fit infinite lines into it provided that we shrink them each time, but at any one time you still have a finite amount of lines.
Maybe 3.3 recurring is a better example? An infinite number of threes after the decimal point, but a finite value (10/3)? Just thinking, I don't know.
I wonder if we could combine this with the "what are you knitting" thread and have an infinite knitted traingle? :lol:
Q. What's the longest song ever?
A. Aleph-zero green bottles hanging on the wall! :wink:
Q. What's the longest song ever?
A. Aleph-zero green bottles hanging on the wall! :wink:
A better one would be:
Aleph-one green bottles hanging on the wall.
(Aleph-one is the cardinality of the real numbers!! Whereas aleph-zero is the cardinality of the natural numbers.)
Ah, but the real numbers are uncountable!
Any area can be cut up into infinite bits. That's why you integrate to find area, duhhhhhhhh :razz:
let i represent infinity:
i*i
what are we saying here?
i+i infinite times
now, imagine instead of infinite times, we do it a finite number of times
let's say 16 times
i+i+i+i+i+i+i+i+i+i+i+i+i+i+i+i
this is the same as:
4i+4i+4i+4i
or:
8i+8i
or:
16i
Basically, we can cut up this large addition into 2 halfs or more. We can also cut it up into infinite halfs in the case of having infinite additions. Infinite halfs are always going to result in the same end number of additions however. 2 seperate halfs of infinity = 2 "infinities". So:
3i+3i==12i+16i==i
No matter how many times you multiply i by itself, or add it to itself (as multiplication is basically addition) you get the same result i.
So, to answer your question - no. Strictly speaking i is not a real number but actually an irrational number.
The real meaning of infinity is autistic pride :wink:
Hurrah! :grin: :smile: :grin:
Negative numbers are best thought of as simple opposites. If you pay me £10, I gain £10 and you lose £10, if you pay me -£10, I lose £10 and you gain £10.