Undergrad Big Bang singularity: can we say anything about its size?

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The discussion centers on the nature of the Big Bang singularity, questioning whether it can be defined as finite or infinite. It suggests that if the singularity is infinite, then the Universe must have always been infinite, complicating the concept of transition from finite to infinite post-Big Bang. The role of cosmological inflation is examined, raising questions about whether the Universe's expansion pertains to volume or spatial dimensions. The conversation references insights from articles on the Big Bang, indicating a need for further exploration of these concepts. Overall, the dialogue emphasizes the complexities surrounding the definitions and implications of the singularity in cosmology.
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Has the Universe been anything other than infinite? (ie finite)
The Big Bang is sometimes described as started from a singularity, which I have interpreted as meaning that its characteristics are undefineḍ. If that is the case, can we not even say that the Universe as a singularity was still infinite? Otherwise we are implying that the singularity was finite, and at some point after the Big Bang, there must have been a point in time when there was a transition from finite to infinite.

Cosmological inflation suggests that the Universe is expanding. Is this by volume? That doesn't make sense to me. If the Universe is infinite in volume, at no point during the inflationary period could it have been anything less than infinite? Or does this suggest that spatial expansion is not related to volume?
 
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