## Can an infinite group has a finite subgroup?

Then the direct sum of the groups in S is an infinite group in which every element has finite order, so generates a finite subgroup. (The direct sum is the set of sequences for which the ith entry is a member of the ith group in S, such that all but a finite number of the entries is the identity of its group.

### When we say an element in a group has infinite order?

In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element.

Does an infinite group have an order?

Hence, every element has finite order but the group is infinite. The identity element ∅ has order 1.

How do you show an infinite group?

A group which is not finite is an infinite group. That is, an infinite group is a group of infinite order. That is, a group (G,∘) is an infinite group if and only if its underlying set G is infinite.

## What is the meaning of infinite group?

In group theory, an area of mathematics, an infinite group is a group whose underlying set contains an infinite number of elements. In other words, it is a group of infinite order.

### What are finite infinite elements?

If a set has the unlimited number of elements, then it is infinite and if the elements are countable then it is finite.

What is a finite and infinite sequence?

Finite sequences are sequences that end. Infinite sequences are sequences that keep on going and going. Examples of finite sequences include the following: The numbers 1 to 10: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

What is finite and infinite example?

A set that has a finite number of elements is said to be a finite set, for example, set D = {1, 2, 3, 4, 5, 6} is a finite set with 6 elements. If a set is not finite, then it is an infinite set, for example, a set of all points in a plane is an infinite set as there is no limit in the set.

## What is a finite and infinite sequences give examples for each?

Finite sequences are sequences that end. Infinite sequences are sequences that keep on going and going. Examples of finite sequences include the following: The numbers 1 to 10: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Our alphabet: {a, b, c, . . .

### How do you write an infinite and finite set?

What are finite infinite numbers?

Is infinity a finite number?

All of these numbers are “finite”, we could eventually “get there”. But none of these numbers are even close to infinity. Because they are finite, and infinity is not finite!

## What is the example of infinite sequence?

An infinite sequence is a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integer s {1, 2, 3.}. Examples of infinite sequences are N = (0, 1, 2, 3.) and S = (1, 1/2, 1/4, 1/8., 1/2 n .).

### Why is infinity finite?

Infinity is not a real number An idea of something without an end. Infinity cannot be measured. Even these faraway galaxies can’t compete with infinity.

How do you make infinity finite?

Outside of fancy philosophical musings, there’s a far simpler way to make something infinite fit within a finite space: Make a fractal, a mathematical set that exhibits a repeating pattern at every scale to infinity!

What is infinite and finite sequence?

Lesson Summary A sequence is a string of things in order. Finite sequences are sequences that end. Infinite sequences are sequences that keep on going and going. Examples of finite sequences include the following: The numbers 1 to 10: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

## What is infinite sequence example?

### What is finite and infinite sequence with example?

What is finite infinite sequence?

A sequence is a string of things in order. Finite sequences are sequences that end. Infinite sequences are sequences that keep on going and going. Examples of finite sequences include the following: The numbers 1 to 10: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}