Can anyone prove the following:
Let g be a real number such that 0 <= g <= 1. Let m,n be integers.
Conjecture 1: a^g + b^g - 1 >= (a+b-1)^g
Conjecture 2: if a >= b, then b^g - (b-1)^g >= a^g - (a-1)^g
Let g be a real number such that 0 <= g <= 1. Let m,n be integers.
Conjecture 1: a^g + b^g - 1 >= (a+b-1)^g
Conjecture 2: if a >= b, then b^g - (b-1)^g >= a^g - (a-1)^g
“The truth of our faith becomes a matter of ridicule among the infidels if any Catholic, not gifted with the necessary scientific learning, presents as dogma what scientific scrutiny shows to be false.”
