ILIEKMATHPHYSICS

Proving limits of sequences from the epsilon-N definition Practice Problems (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Proof that 1^b = 1 for every rational number b (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Proof that (ab)^c = a^c b^c for rational exponents (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Proof that (a^b)^c = a^bc for rational exponents (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Proof that a^b a^c = a^(b+c) for rational exponents (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Defining rational number exponents (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Prove that (nth root of x)^m = nth root of x^m (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Prove if a ≥ 0 and n is an integer ≥ 0, then a^n ≥ 0 (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Prove x﹤y if and only if nth root of x﹤nth root of y (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

If x﹥1 then nth root of x﹥1, and if 0﹤x﹤1 then 0﹤nth root of x﹤1 (Proof) (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Prove that the nth root of 1 is 1 (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Prove that the nth root of xy = nth root of x times nth root of y (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Prove that the mth root of the nth root of x equals the mnth root of x (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

If a ≥ 0 and a^n = x, then a = nth root of x (Proof) (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Prove that x = (nth root of x)^n (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Prove that the nth root of a positive number is positive (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Prove that the nth root of 0 is 0 (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Defining the nth root of x as the supremum of {y ≥ 0 y^n ≤ x}, proof it exists (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Let a,b ≥ 0 and let n ≥ 0 be an integer. Prove if a ≤ b then a^n ≤ b^n (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Let 0 ﹤ a ≤ 1 and m,n be integers. Prove if m ≤ n then a^n ≤ a^m (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Let a ≥ 1 and m,n be integers. Prove if m ≤ n then a^m ≤ a^n (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

If a ﹥ b ﹥ 0 and n is a positive integer, then a^n - b^n ≤ (a-b)na^(n-1) (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Proof that 0 to the power of n equals 0 (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Let 0 ﹤ a ﹤ 1 and m,n be integers. Prove if m ﹤ n then a^n ﹤ a^m (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Let a ﹥ 1 and m,n be integers. Prove if m ﹤ n then a^m ﹤ a^n (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Let a,b ≥ 0 and n be a positive integer. Prove if a^n = b^n then a = b (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Let a,b ≥ 0 and n be a positive integer. Prove if a^n ﹤ b^n then a ﹤ b (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Let a,b ≥ 0 and n be a positive integer. Prove if a ﹤ b then a^n ﹤ b^n (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Proof if 0 ﹤ a ﹤ 1 then 0 ﹤ a^n ﹤ 1 for every positive integer n (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS

Proof if a ﹥ 1 then a^n ﹥ 1 for every positive integer n (ILIEKMATHPHYSICS)

ILIEKMATHPHYSICS