Natural Numbers and Integer Properties Quiz

Which property of natural numbers ensures that the sum of any two natural numbers is also a natural number?

What property is illustrated by the equation $a + (b + c) = (a + b) + c$ for natural numbers a, b, and c?

Which property of natural numbers states that the product of any two natural numbers is also a natural number?

What property is represented by the equation $a \cdot (b + c) = a \cdot b + a \cdot c$ for natural numbers a, b, and c?

Which of the following is NOT a property of integers?

What property of the integers ensures the existence of a unique number called the multiplicative identity?

Which property of integers states that the order in which numbers are added doesn't change the result?

What is the set of integer numbers denoted by?

Which property states that for any two integers, their product is also an integer?

What does the Additive Inverse Property state for all integers?

Which property guarantees that for any integers a, b and c, the equation a · (b + c) = a · b + a · c is always true?

Which property states that the order in which you multiply two integers does not affect the result?

Which of the following properties is NOT applicable to rational numbers?

Which property allows us to group integers in multiplication without changing the outcome?

Which property states that for any integer 'a', there is a unique integer '-a' such that their sum is zero?

Which property guarantees that for any two numbers, there is a unique number that, when added to the first number, results in the second number?

Which of the following inequalities is true for all positive integers n?

What is the value of n for which the following inequality is true: $\frac{1}{4} + \frac{1}{9} + ... + \frac{1}{n^2} ≤ 2 - \frac{1}{n}$ ?

What is the value of the expression $(1 + x)^n$ for a real number x > -1 and a positive integer n, according to Bernoulli's Identity?

For what nonnegative integers n is the expression $5n-1$ divisible by 4?

For what nonnegative integers n is the expression $10^{n+1} - 9^n - 10$ divisible by 81?

For what nonnegative integers n is the expression $32^n - 2^n$ divisible by 7?

What is the base case for the following statement: For every nonnegative integer n, 2n > n?

Which of the following is the correct inductive step for the statement: For every nonnegative integer n, 2n > n?

What is the minimum counterexample that can be used to prove that 6 | 7n(n^2 - 1) for every positive integer n?

What is the minimum counterexample for the statement that 3|(2^$2n$ - 1) for every positive integer n?

What is the base case for the statement: For every integer n ≥ 5, 2n > n^2?

Which of the following is the correct inductive step for the statement: For every integer n ≥ 5, 2n > n^2?

What is the base case for the statement: For every nonnegative integer n, 3 | (2^(2n) - 1)?

Which of the following is the correct inductive step for the statement: For every nonnegative integer n, 3 | (2^(2n) - 1)?

Which of the following set(s) is/are well-ordered?

Which of the following statements accurately describes the result of adding 1 + 3 + 5 + · · · + (2n − 1) and (2n − 1) + (2n − 3) + · · · + 1 ?

Which of the following is the correct formula for 1 + 4 + 7 + · · · + (3n − 2) for positive integers n?

What does 13 + 23 + 33 +...+ n3 represent geometrically?

Which of the following formulas represents the sum 1 · 3 + 2 · 4 + 3 · 5 +...+ n(n + 2) for every positive integer n?

Given that r ̸= 1 is a real number, which of the following formulas represents the sum a + ar + ar 2 +...+ ar n−1 for every positive integer n?

Consider the following sequence: 1/3·4 + 1/4·5 + 1/5·6 + … + 1/(n + 2)(n + 3). Which of the following formulas represents the sum of this sequence for every positive integer n?

For which integer values of n is the inequality 2n > n3 true?

What is the name given to the number 1 in the Multiplicative Identity Property?

Which property states 'For all a, b, c ∈ Q, if a < b and c > 0, then ac < bc'?

What is the set of all rational and irrational numbers called?

Which of the following is NOT an irrational number?

What is the 'Well-Ordering Axiom'?

What is the first step in proving a statement using the Principle of Mathematical Induction?

What is the formula for the sum of the first n squares?

What is the starting value for proving the statement '1 + 2 + 3 +...+ n = n(n+1)/2' using mathematical induction?