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A semiprime (also called a 2-almost prime) is an integer that is the product of exactly two primes (possibly the same). The first few are 4, 6, 9, 10, 14, 15, 21, 22... Can you prove that there are infinitely many semiprimes. Assume there are n primes, then the number of semiprimes is the combination of n things taken two at a time, or n!/2!(n-2)!, or n(n-1)/2. Of course, the number of primes (n) is infinite, and so is n(n-1)/2. There are infinitely many semiprimes.
Infinity+1 is infinity, not a greater infinity, but the same infinity. Here we have an infinite set of numbers which seems vastly larger than another infinite set of numbers. One set contains n (infinity) numbers and the "bigger" one contains (n-1)/2 times that many. We will see this idea later, when I write articles on infinity and on transfinite numbers. For the time being, just note that these are the same infinities.