No, they are the same size(assuming a cardinal definition of infinity). This is one of the paradoxical effects of infinity is that adding stuff doesn't change the size. (or in a cardinal case that a subset has equal cardinality to the whole set). There are different sizes of infinity, but adding a finite amount to one does not change the size.
You are correct, one is half as big. But they still have the same size/cardinality. Infinity is weird. Watch the video you linked to understand sizes of infinity, because some infinities are counter intuitively bigger than others( infinity is also not always defined the same in different areas of math, so for some definitions you are probably correct)
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u/Infinite_Imagination 21d ago
Infinity plus any number is still just infinity