The Return of Discussions for the sake of Kermi3

well, Kermi wanted to see some good discussions going here again...so I will start one...

This is about mathematical theory.

Many like to view mathematics, or numbers rather, as a circle.

Since numbers are infinite, and have no end, many like to view numbers as an endless circle....almost like a recursive function with no exit condition. the number line is viewed as continuously going around that circle.

others view it as just an endless line....with simply no end...this view originally spawned the circle view...as many people believe that the two ends of the line would eventually hit each other...

another view is the figure 8 theory...with positive numbers on one end of the 8, and negative numbers on the other end of the 8...

which theory do u like? and give support for your theory.

by the way, i like the figure 8 theory.

I was having a discussion with one of my friends about this a couple years ago online, and we were discussing it. We at first thought of it as a circle, but then I proposed to him that it could be viewed more rather as a figure 8, rather than a circle...

we liked the idea of having the positive numbers on one circle and the negatives on the other, and the two circles connecting at the center in a figure 8 form...

the connection between two of the ends is obviously the number 0, and the other connection would be infinite...

i believe in the infinite line theory. there's no need for a more complicated model for real numbers.

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as many people believe that the two ends of the line would eventually hit each other

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this would require proof that +infinity == -infinity.

Prehaps because it is what I was always brought up on, but i prefer the line to. Although the 8 does have appeal.

And I think i opened a pandora's box!

i would say the figure eight works out good for computers, since signed integer loop back around into negatives...

the circle would have to be a spiral to be endless.

for me, the line fits best.

what about imagenary numbers? and then you got things like "5 + 2i", etc... middle of the circle/figure 8?

To me, it does not make very much sense to think of numbers "residing" on a line, circle, etc. The concept of "number" is too abstract for there to be any meaningful relation between it and space. It is like asking where is the location of the soul, etc.

placing numbers in any figure is just purely ridiculous. Placing numbers on a line is no more accurate then trying to picture a 1 dimensional figure.