Meep's Math Matters 3: infinitude of primes

[xXSabzzXx]

Missed my math lecture today, but I think I wouldn't have understood it as well as watching this.

[meepsmathmatters]

@xXSabzzXx thanks for the kind words!

[KillingKunoichi]

Meep, are you a MAth teacher or are you really a Math Prodigy?!

[meepbobeep]

I'm a teacher. Been teaching math for quite some time now.

Really need to get back to making these vids when I have the time.

[SnapeHalfbloodPrince]

You gave me a reply about tne number zero, And I am not a good math student, but waht about their negative brothers? do they have the same way of calculating or are they just imaginary?

[meepbobeep]

Calculating what about negative numbers?

Much of math is by exact definition, and prime numbers by definition are positive whole numbers, greater than one.

If you want to factor out negative numbers, first you pull out -1 as a factor (I'll do an example: -35 = -1 * 35 = -1 * 7* 5), then you can pull out its prime factors.

[sp0ngcl0ng]

oh you're a good math student huh?

who cares about that?

[SnapeHalfbloodPrince]

what is with the number zero?

it is only dividable by itself not by one....and if you divide any other number by 0 there is 0 left...

[meepbobeep]

Generally one requires the number to be a positive whole number, greater than 1. It's a matter of definition, and what's useful.

Mathematical definitions are arbitrary, and the math conventions do not allow 0 to be prime, because there's no use in saying 0 is prime and then excluding it explicitly in all the theorems dealing with prime numbers.

[ivolol]

You can't divide by 0, full stop. No matter how many 0s you mutiply together, they will never amount to anything but 0, so the question is pointless. 0 can be divided by any number you wish. Zero of that number will divide into 0. :)

[7x34hj]

@SnapeHalfbloodPrince Zero is not divisible by zero; as with any other integer dividing by zero tends to infinity. I hope this helps :)

[RassilonSix]

Very nice; this and "Irrationality of Square Root of 2" are two of my favorites because they're so easy to explain to others.

How about "The cardinality of the set of real numbers is greater than the cardinality of the set of integers"? That's the one I would like to see next.

[dustmallmmm]

Or even simpler: for any finite collection of primes take their product and add 1, just as Euclid did? He didn't use any inderect arguments.

[meepbobeep]

What you described is pretty much the exact same argument, with a minor detail changed. Either way, there's a prime p larger than what you named the "largest" prime before. The logical structure is exactly the same.

[dustmallmmm]

Here is a streamlined argument that does not use an argument by contradiction. Take any number A. Then A!+1 is either prime or is divisible by a prime B that must be greater than A. Therefore the collection of all primes can not be finite.

[dustmallmmm]

Why did you have to use the argument by contradiction?

Could not you just show that for any finite collection of primes there is a prime that is greater than all of them, by the very same argument that you used? That would be enough to demonstrate the infintude of primes, right?

[googillion]

Yes, there is no end to prime numbers. Is there a finite number of perfect numbers? I think not. Nice vid.