Prove by direct proof that any integer n ≥ 3 can be part of a Déjà vu Pair n = [11 · · · 1]b for some base b ≥ 2. Use written paragraph format.

Show that V3+2/6 is an irrational number.

2. Let x be irrational real number. Prove that 2x+3 is irrational

Please help me to write this as a proof.  Let n be an integer. If n is the sum of three consecutive integers, then 3 | n

Graph on the number line, and express in interval notation. The set of all real numbers between 1 and 2 including both - 1 and 2. Choose the correct graph below. O A. O C. ← -6 -6 -5 + -5 -4 -4 -3 -3 -2 -1 0 2 3 3 4 + 4 + 5 5 C 6 O B. O D. ← -6 ← -6 + -5 + -5 -4 + -4 -3 -3 -2 -2 -1 0 0 2 2 + 3 3 4 5 + 5 + 6

let a and b be real numbers. Prove by contraposition that, if a + b is greater than or equal to 100, then a > 39 or b > 60

Show that 5 – V is algebraic number.

Suppose that a positive number a is written in scien- tific notation as a = c × 10", where n is an integer and 1 sc< 10. Explain what n indicates about the size of a.

State Archimedean property of real numbers. Hence show that for each real number ɛ >0, there exists a positive integer m such that -<ɛ for each n2m.

For all integers a, b and c, if a divides b and a divides c, then a divides (4b - 3c). True False