Flirting with Infinity

Have you got your pinny on yet?

Sort of. But the thing is, you can't have the concept of a straight line without taking into account the topology of the space it's drawn within. Most people will automatically default to a flat Euclidian plane, but that's only one of many topologies. But it's perfectly possible to have a straight line on, say, a saddle seat, a sphere, a dodecahedron, a cylinder, or whatever. They will all be perfectly straight lines that appear, to the benefit of our 3-dimensional view, to curve or bend - but are 100% perfectly straight with no bends in their own topologies.

Back...way back when with the 2D stuff, I said it was impossible. I stand by that.

In fact, even in 3D space, a circle with infinite circumference is impossible.

Agree 100%, no matter how much the OP thinks his nonsensical rantings are enlightening and opening the minds of us smelly, caged beasts.

The Klein bottle was first depicted in post #36 of this Thread. You might need to read up on the thread, to catchup on what's already been discussed.

"Us caged beasts." ??? No, it wasn't plural.

So if I try to simplify that...I end up with.

"A straight line is only straight relative to the observer within the lines topology(?) space (?)"

And you didn't understand what I meant.


8)

Yes, I'd say that's accurate.

The concept of "straight" can only apply to the topology of the space or plane being discussed.

I understood it as, it is always straight along one axis, its is curved on another...i think.

Both are impossible end of

Both are impossible end of

We haven't read this whole thread, so somebody may have already said this.

We don't know if all infinities are equal, so we don't know if the line is the same or different than the diameter of the circle.

If they are the same then the difference is:

difference = pi*d - d

difference = d(pi - 1)

Any number times an infinity must be an infinity so:

difference = d

Any number times an infinity must be an infinituy so:

difference = d - d = 0

therefore 0 = infinity.

Maybe infinities don't obey the distributive law.

Infinity is an idea. It is a representation, an indicator. It is completley different from other numbers like 1, 4000, 4.5, 100000000000000000000000000000...a hundred times(google) because it is by defintion beyond human capacity to measure! We also have another such number at the other end ofthe spectrum-"zero". Zero is not a number, it is the mathematical representation of "nothingness". Both infinity and zero are immensely useful "ideas" in math.

Homo sapiens understood the idea of infinity early in prehistoric times because God is "boundless power and consciousness and immortal". Nowadays we call God, infinity
However it took several thousands of years to discover zero. Aryabhatta, an indian mathematician is credited to have given "nothing" the name, zero! Suddenly and surely, mathematics simplified a thousand-fold; if you know people's names you can call them whenever you need them
He used zero(actually nothing) to develop the decimal system notation that we still use. Aryabhatta had "noting" to offer and we accepted it with the deepest gratitude!

perhaps britneylulu meant to point out in the post above that infinity, by definition, immeasurable. To apply even well known mathematical properties to it would result in disaster-like:

therefore 0 = infinity

and other problems like, 4 angles in a triangle, 360 degress in a triangle, a point becoming a line, etc.
all are examples of reductio ad absurdum. If your intial premises are false, your conlcusion will be ridiculous!

My humble conclusion: Mathematics is pure science-a thought-world and in it we have a God. His name is INFINITY!