playerqq

> I want Stadia. I've read reviews yesterday and was amazed by the lack of a long term vision from the reviewers. If Google doesn't drop the ball (which is a huge if knowing the company's history), Stadia makes a lot of sense.

I disagree that the reviewers lacked long term vision. Nearly all of seem to have been burned by the promise of videogame streaming before, and the current state of Stadia only inspires cautious optimism at best.

You're right that everybody wants to live in a world where videogames stream anywhere at 4k+ and 60+fps with minimal latency. But OnLive was 2010. Gaikai was 2012, followed by Playstation Now in 2014. This space isn't a greenfield for lack of trying.

Furthermore, with initiatives by Microsoft (Project xCloud) and EA (Project Atlas), there's no reason to accept Google as the standard bearer for game streaming. There's plenty of companies that could be coming up with the experience we've been waiting a better part of a decade for.

But let's say our "gender-bias free" method leads a manager to hire 7 men and 3 women. This leads the manager to draw the conclusion that "My next hire is more likely to be a male than a female". The manager wants to acquire a good candidate pool as quickly as possible, so now he changes his mental search heuristic to favor male applicants, if he can discern their gender.

Haven't we just reinforced his bias further, now cemented by hard fact (and faulty reasoning)?

edit: missed a word

Got it. I was trying to do a proof while avoiding abstract algebra as much as possible, given how rusty I am with it.

Thanks for the feedback, and additional things to take a look at!

I haven't looked at any proofs for the FTA. Could somebody point out if I made any mistakes on the one I've arrived at?

[1] Proof by induction that if a positive integer has a prime factorization, then it is unique.

We're inducting over Z_N, where Z_N is the set of all positive integers with at least one known prime factorization using exactly N number of primes. Call this factorization Pn = p_1 * p_2 * ... p_n

For every case, split into proof by cases and contradiction: suppose there is an element Z in set Z_N had another factorization Fn.

- If Fn has the same number of factors as Pn, divide both sides by p_i. Since Fn / p_i must be an integer, Fn must contain p_i, or else one of its factors f_i actually isn't prime by Euclid's Lemma.

- If Fn has k more factors than Pn, then divide Pn by (f_1 * f_2 * ... * f_n). Then (f_n+1 * ... * f_n+k) = X for some composite integer X > 1. Thus Fn = X * (f_1 * f_2 * ... * f_n) = (p_1 * p_2 * ... * p_n) = Pn. Since (p_1 * p_2 * ... * p_n)/Z must be an integer, Z must divide into one of the factors p_i by Euclid's lemma, which is impossible since they are prime by definition.

- Similar argument to above if Pn has more factors.

[2] Proof by contradiction: Every positive integer Y greater than one has a prime factorization.

Suppose not. We know Y = Y * 1. So Y must be composite in order for it to not have a prime factorization. Hence, we know that Y = a * b, (a, b > 1). At least one of the two must be composite or else Y has a prime factorization, so let's say (a) is composite. Then a = c * d (c, d > 1). Then at least one of the two factors must be non prime or else we've found the prime factorization for Y. Repeat ad infinitum to show that if Y does not have a prime factorization, then it must be the product of an infinite number of composite factors, with every factor great than 1. Hence contradiction.

So every positive integer greater than 1 has a prime factorization, and it must be unique.