Explanation

The set of integers, Z, forms a group under addition.

Explanation

Square root is a unary operation because it takes only one argument or input, whereas addition and multiplication are binary operations that require two inputs.

Explanation

The p-series is a series of the form:

1 + 1/2^p + 1/3^p + 1/4^p + ...

The p-series is convergent if p > 1. If p ≤ 1, the series is divergent.

Explanation

The formula for the volume of a solid of revolution around the x-axis is π ∫[a, b] (f(x))^2 dx, where f(x) is the function being rotated, and a and b are the limits of integration.

Explanation

• A convergent sequence in a metric space is bounded.
• This means that the sequence has a finite limit, and all terms of the sequence are within a finite distance from this limit.
• As a result, the sequence is bounded, meaning it has a finite upper and lower bound.

Explanation

The correct answer is: Xn < X(n+1)

A sequence (Xn) in a metric space X is said to be strictly increasing if for all n, Xn is less than X(n+1), denoted by Xn < X(n+1). This means that each term of the sequence is strictly greater than the previous term.

Explanation

Ext(A) denotes the exterior of the set A, which is defined as the interior of the complement of A, i.e., Int(A^c).

Explanation

A subset F of a topological space X is closed if and only if F is equal to its closure, denoted by Cl(F).

Explanation

• A group of prime order (a group with a prime number of elements) is always a cyclic group.
• This is a fundamental result in group theory, known as Lagrange's theorem.

Explanation

• A cycle of length 2 is called a transposition.
• A transposition is a permutation that swaps two elements, leaving the others unchanged.
• For example, the permutation (1 2) is a transposition that swaps the elements 1 and 2.