# Which is closer to 16: 32 or 17?

In a +1 way, it’s 17.

But in a PRIME FACTOR way, it’s 32.

Why? And which is it?

• Kindergarten kids: 17
• Primary: 17
• Middle School: 17
• High school: 17
• College: probably both, but more likely 17
• University: 15? 17? 32? WHAT?!?!?!?!
• Real-life mathematicians who only care about supernaturals: 32

(screech sound)

What on Earth is a SuPeRnAtUrAl?!?!?!?!?!?!?!?!

If you watch Vi Hart’s video “How many types of infinity are there?” at 9:04, it says “supernatural” numbers. You know indices, x to the power of y? if y is infinity, for any real x bigger than 1 will be infinite. The +1 definition sees 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*… the same as 7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*…, but in the supernaturals, the 7*7*7*7*7*7*7*7*7*7*… is bigger, because they are multiplied the same infinite amount, and every time, 2<7, 4<49, etc.

So in the supernatural way, the number 16 is closer to 32 than 17 because 16 and 32 are just times 2 away, while 17 is… well, does not have a common factor at all.

That’s good!

Q.E.D.