&gt; There is very little that is logical about infinity itself ...<p>On the contrary, infinity is a very logical notion -- much more logical than many other ideas we accept. For example, what value must &quot;m&quot; have for this statement to be true:<p>sum(n:1 to m inclusive, 2^-n) = 1 (i.e. 1&#x2F;2 + 1&#x2F;4 + 1&#x2F;8 ...)<p>What value must &quot;m&quot; have, for this statement to be true:<p>lim(n -&gt; m), (1+1&#x2F;n)^n = e (base of natural logarithms)<p>For both these examples, for the described outcomes, m must equal infinity.<p>Also, you say, &quot;For example, the Universe is &#x27;infinite&#x27; yet it is also expanding&quot;, but you also say, &quot;It took a couple thousand years just for mathematicians to theoretically prove that some infinities are larger than others ...&quot; If one infinity can be said to be larger than another, then this admits the possibility of any single infinity expanding.<p>Imagine a cube of space, in isolation, initially measuring one meter in any of its dimensions. If measurements reveal that this value is increasing over time, one may conclude that the cube is expanding. Now imagine that the cube is embedded in a space consisting of an infinity of such cubes in three spatial dimensions, all increasing in size in the same way. Does the fact that the cube is part of an infinity of such cubes prevent it from expanding? If this were true, it would be an easy test of the existence of an infinite spatial manifold -- but the idea of an expanding infinity is logically consistent.