Infinities: More Than One
summary
Shows concrete pairings and a counting method so equal sizes become provable: naturals pair with evens by double map, naturals enumerate all integers via a zigzag enumeration, rationals sit on a p/q grid traced in a diagonal path while skipping repeats to get a bijection, and Cantor’s diagonal constructs a new real whose nth digit differs from the nth listed real so no listing covers all reals. Concludes reals are strictly larger than naturals and hints at the continuum question.
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