# One Thing I Believe, One Thing I Know, One Thing I Doubt

### I Believe

I believe that Tom Brady & Bill Belichick are both the biggest cheaters in the NFL today. I believe this because both deflategate and spygate are evidence of the pair both being cheaters. Also Bill Belichick always wears that nasty sweater so he obviously is a cheater.

### I Know

I know that 1+1=2 because there is proof behind it being true. Also 1+1=2 is excepted by basically anyone in the world. Lastly the only way to prove that 1+1≠2 is to use different definitions of integers.

The proof starts from the Peano Postulates, which define the natural

numbers N. N is the smallest set satisfying these postulates:

P1. 1 is in N.

P2. If x is in N, then its “successor” x’ is in N.

P3. There is no x such that x’ = 1.

P4. If x isn’t 1, then there is a y in N such that y’ = x.

P5. If S is a subset of N, 1 is in S, and the implication

(x in S => x’ in S) holds, then S = N.

Then you have to define addition recursively:

Def: Let a and b be in N. If b = 1, then define a + b = a’

(using P1 and P2). If b isn’t 1, then let c’ = b, with c in N

(using P4), and define a + b = (a + c)’.

Then you have to define 2:

Def: 2 = 1'

2 is in N by P1, P2, and the definition of 2.

Theorem: 1 + 1 = 2

Proof: Use the first part of the definition of + with a = b = 1.

Then 1 + 1 = 1' = 2 Q.E.D.

Note: There is an alternate formulation of the Peano Postulates which

replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the

definition of addition to this:

Def: Let a and b be in N. If b = 0, then define a + b = a.

If b isn’t 0, then let c’ = b, with c in N, and define

a + b = (a + c)’.

You also have to define 1 = 0', and 2 = 1'. Then the proof of the

Theorem above is a little different:

Proof: Use the second part of the definition of + first:

1 + 1 = (1 + 0)’

Now use the first part of the definition of + on the sum in

parentheses: 1 + 1 = (1)’ = 1' = 2 Q.E.D.

-Doctor Rob

### I Doubt

I doubt that the conspiracy that the Moon does not exist is true. There is way too much solid evidence of the Moons existence for it to not exist. Also to always have a hologram of a Moon in the sky would be expensive and difficult to manage. Lastly the best argument for the Moon not existing is that “you can see it”