Infinity Times Zero is Not Zero

The problem is that the laws of addition and multiplication you are using hold for natural numbers, but infinity is not a natural number, so these laws do not apply. If they did, you could use a similar argument that multiplying anything by infinity, no matter how small, gives infinity, thus ∞×0=∞. More sophisticated arguments can also be made, like ∞×0=limx→∞(x×1/x)=1. Clearly all these different values for ∞×0 mean that ∞ cannot be treated like other numbers. In order to ...

 Proof That the Set of Prime Numbers is Infinite

Theorem: There are infinitely many prime numbers. Proof: Suppose, contrary to the theorem, that there is only a finite number of primes. Thus, there will be a largest which we can call p. Now define a number n as 1 plus the product of all the primes: n = (2 X 3 X 5 X 7 X 11 X...X p) 1 Is n itself prime or composite? If it is prime then our original supposition is false, since n is larger than the supposed largest prime p. So now let’s consider it composite. This means that it must be div...

 Radio Telescopes as the Stethoscope Observing the Universe

When they [radio astronomers] grew weary at their electronic listening posts. When their eyes grew dim with looking at unrevealing dials and studying uneventful graphs, they could step outside their concrete cells and renew their dull spirits in communion with the giant mechanism they commanded, the silent, sensing instrument in which the smallest packets of energy, the smallest waves of matter, were detected in their headlong, eternal flight across the universe. It was the stethoscope with w...

 Inscriptions on the Georgia Guidestones

Maintain humanity under 500,000,000 in perpetual balance with nature. Guide reproduction wisely - improving fitness and diversity. Unite humanity with a living new language. Rule passion - faith - tradition - and all things with tempered reason. Protect people and nations with fair laws and just courts. Let all nations rule internally resolving external disputes in a world court. Avoid petty laws and useless officials. Balance personal rights with social duties. Prize truth - beauty - love ...