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So, if I get this thing right, the infinite sum of 2k-spheres where the volume of each goes to 0 as k goes to infinity, is not infinite?
We're not adding up an infinite number of *infinite* dimensions spheres (k-> infinity), we're adding up all k dimensional spheres.
In each k-dimension space there's only one unit sphere. We're summing the volumes of all those spheres for all possible 2k spaces correct ?
That’s right.. sorry if my wording was a bit awkward
OK, got it, thanks!
Linked to the curse of dimensionality?pic.twitter.com/5eiD3ulZbB
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If you sum over the volumes of all 2k-dimensional unit spheres, that sum converges to e^π.
I have no idea why this should be true..
