One infinity is not "bigger" than the other and one set is not "bigger" than the other in the conventional sense of the term. I guess they maybe use that term in the videos or in articles to try and explain the idea and give a feel to people of what cardinality and numerosity of infinite sets means. It is extremely difficult to explain math and physics concepts to non mathematicians with every day language and without equations and mind boggling definitions, that is why they used this term "bigger" which, strictly speaking, is incorrect.
It is however correct to say that one set is more numerous than the other or that one set has bigger cardinality than the other if you stick to the definition of numerosity and cardinality that mathematicians have adopted for infinite sets, to extend as naturally as possible these notions from finite sets to infinite sets.
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