Theorem : All positive integers are equal.
Theorem : All positive integers are equal.
Proof :
Sufficient to show that for any two positive integers, A and B, A = B. Further, it is sufficient to show that for all N > 0, if A and B (positive integers) satisfy (MAX(A, B) = N) then A = B.
Proceed by induction.
If N = 1, then A and B, being positive integers, must both be 1. So A = B.
Assume that the theorem is true for some value k. Take A and B with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence (A-1) = (B-1). Consequently, A = B.
The shortest math joke
The shortest math joke ever: let epsilon < 0 (*)
A biologist, a statistician and
A biologist, a statistician and a mathematician are on a photo-safari in africa. They drive out on the savannah in their jeep, stop and scout the horizon with their binoculars.
The biologist : “Look! There’s a herd of zebras! And there, in the middle : A white zebra! It’s fantastic ! There are white zebra’s ! We’ll be famous !”
The statistician : “It’s not significant. We only know there’s one white zebra.”
The mathematician : “Actually, we only know there exists a zebra, which is white on one side.”
Theorem: All positive integers
Theorem: All positive integers are interesting.
Proof: Assume the contrary. Then there is a lowest non-interesting positive integer. But, hey, that’s pretty interesting! A contradiction.
What is “pi”?
What is “pi”?
Mathematician: Pi is thenumber expressing the relationship between the circumference of a circle and its diameter.
Physicist: Pi is 3.1415927plus or minus 0.00000005
Engineer: Pi is about 3.
