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are something and nothing the same "thing"? if is something infinitely small is equivalent to nothing then what are the implications of this?

in regards to the the universe v.s before big bang nothingness

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They are different. As a quick example, in non-standard analysis we use "infinitesmals", e.g., dx, dy, as somethings. Also, I'm not sure that there was NOTHING before the big bang. Lawrence Krauss has a new book on just this issue.

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Different. Nothing is not a thing, so it can't be equal to anything. In the physical world "something infinitely small" has no sense, that's a mathematical concept.

The Big Bang theory explains what happened from a point in time when all matter was condensed in a extremely hot state. It says nothing about what happened before. Sadly, the information about that "before" is lost, so we will never have evidence of what happened, be it the Big Crunch or a wizard pulling matter out of nothing.

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