No, it doesn’t have to go on forever. In fact, I can use mathematical proof by induction to prove that I am right in all cases.
Mathematical induction is a method for proving that a statement P(n) is true for every natural number n that is greater than k, that is, that the infinitely many cases P(0),P(1),P(2),P(3), … all hold.
This is done by first proving a simple case, P(0), and then assuming that the case P(k) is true and proving that the next case P(k + 1) is also true.
The first step proves the statement is true for k = 0.
The second step proves that if the case holds for n = k then it must also hold for n = k + 1.
Those two steps prove that the statement holds for all natural numbers where n >= k.
Got it?
Try to keep up.
For the first step of the inductive proof we can prove that my assertion for k = 0, basically that I draw you, is obvious because if I haven’t drawn you, then there is no you to draw you.
For the second step, where you are drawing you, I can always demonstrate that I drew you drawing you, and if you add another you drawing you I can always assert that I drew you drawing you before you drew you since you are a cartoon character that I invented and draw.
Therefore, it is proven that no matter how many times you show a picture of you drawing you it is true that I always had to previously have drawn you doing that…. no matter how many times you try that trick.
There!
Waddaya think of that?
