Re: Two results of set geometry

David R Tribble wrote:
[Yeah, I know there have already been other responses to this.]

stephen@xxxxxxxxxx wrote:
I am saying that a sqaure of finite dimensions is not infinitely tall.

Tony Orlow wrote:
You are being woefully unimaginative. Picture a square of infinite
dimensions [sic], consisting of unit squares of uncountable number.

If it's infinite, it doesn't have any edges, so how do we
know it's an infinite square, and not, say, an infinite
triangle or pentagon? Or circle?


Why doesn't it have edges. Does an infinitesimal square have edges? What is the definition of "square", as opposed to "finite square"?


Now, zoom
infinitely out, so that you can actually see the square, such that it
appears to be one unit in size.

How is that done? If it's infinite in extent, there is no
vantage point from which it doesn't look infinite in both
directions. Are you saying it's not really infinitely wide?

Sure it is, but you are at an infinite distance, and therefore it's all viewable.


But assuming that "zoom infinitely out" has meaning,
wouldn't the square (which everyone else would call
a "plane") look like a single point when viewed from
an infinite distance?

No, because it is infinitely wide. If the width is x and you are x distance from it, it will cover only a finite angle from your viewing angle. Why is that different for infinite x?



At this point, the unit squares of which
it consists have shrunk to infinitesimal elements, as the infinite
square has shrunk to a finite size.

So now we can see edges of the square?

Yes, we are infinitely distant, so we can see the entire extent of the infinite square.

How many
points are on those edges?

Big'Un, let's say.

And what about the
center of the infinite square?


What about it?

Peace,

Tony
.

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