MPSI 1 Math Homework: Real Numbers, Functions, Logic

∀x∈R,∀y∈R,x2< y2y < 0⇒y < x
∀a∈R,∃b > 0, b > a
∀x∈R,(∃ε > 0, x > ε)⇔x > 0
∀x∈R,(∀ε > 0, x 6ε)⇒x60
∀x∈R,(∀ε > 0, x >ε)⇒x>0
fR R
∀x∈R,∀y∈R, f(x)f(y)−f(xy) = x+y.
fZ
∀n∈Z, f(n) = (n−10 n > 100
f(f(n+ 11)) n6100.
f(101), f(100), f(95), f(91)
f(n)n6100