Extraordinary claims require extraordinary evidence. Can you cite any claims by mathematicians that there were "gaps"? It isn't even true for rational numbers that you can identify an unoccupied "gap".

▲

Quekid5 2 hours ago | parent [-]

sqrt(2)

▲

bhk 2 hours ago | parent [-]

That's not a "gap" that you find by "zooming in". And how can it be a gap when it is occupied?

	▲	an hour ago \| parent \| next [-]
		[deleted]
	▲	an hour ago \| parent \| prev [-]
		[deleted]