Quote:
Originally Posted by N1
I understand the Universe is infinite in a similar way a circle or spherical surface is infinite. Reduce its diameter, and it's still infinite. Reduce it to a dimensionless point and it's still infinite because it lacks dimension. So at no stage was it finite.
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The spherical surface is finite but unbounded. It has a finite surface area for any given radius.
Similarly the circumference of a circle, is finite for any given radius.
For an n-dimensional hypersurface to be infinite means it cannot be enclosed in an n+1-dimensional "ball". In 2 dimensional Euclidean space the ball is a circle, in 3 dimensional Euclidean space a sphere etc. We can make the radius of the ball as large as we want, there will always be points on the infinite surface that lie outside the radius of the ball.
Regards
Steven