let Pn be the statement that "Pn > Pn-1, such that it is the nth day of your life, where n = 0, ... last day of your life"
intuitively,
P1: This is the day you were borned
Pk: This is the kth day of your life
When n = 0, P1 > P0 is true, since obviously, if you are not borned, you have no life, so first day of your life is better than before you were borned.
Assume n = k is true, i.e. Pk > Pk-1
when n = k+1, RHS = Pk
LHS = Pk+1
= Pk 's tomorrow
As the saying goes, "Tomorrow will be a better day!"
Therefore Pk+1 is a better day than Pk, i.e. Pk+1 > Pk (Proven)
So, by M.I. the last day of your life is the best day of your life.
Is this proof sound and complete? Though I forgot what sound and complete means..
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