# Concept of Infinity in Mathematics

*I am a PhD student of mathematics. I have complete MS in math from the University of Pakistan and have been writing online since 2020.*

## Concept of Infinity in Mathematics

## Concept of Infinity in Mathematics

**Introduction:**

Everywhere in mathematics, even in fields like mathematical physics that use the idea of infinity and the operation of infinite sets have been used. The idea of something being limitless, boundless, or without boundaries.

English mathematician John Wallis created the standard sign for infinity, in 1655. The term "infinity" in mathematics refers to something that is larger than a real number. It typically refers to something without boundaries.

This idea, which is applicable in a variety of subjects, is most frequently employed in the domains of mathematics and physics. The word "infinity" is likewise acceptable when referring to the extended real number system.

**Definition:**

The concept of infinity refers to something that has no beginning or end. It is generally something that has no restrictions. It is a condition in which there are no boundaries in regard to time, space, or any other kind of dimension.

**Symbol of Infinity:**

The symbol of infinity used commonly is ∞. In the middle of the sixteenth century, Wallis used the symbol for infinity that is used today, He also developed the concept of 1/ for an infinitesimal, which is a unit of measurement lessness.

The infinity symbol, which resembles a horizontal form of the number 8, stands for immortality, endlessness, and infinity. However, some scientists claim that John Wallis might have taken inspiration for the infinite symbol from the Greek letter

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**Properties of Infinity:**

There are four basic properties of infinity.

- Addition property of Infinity
- Subtraction property of Infinity
- Multiplication Property of Infinity
- Quotient Property of infinity:

**Addition property of Infinity:**

Suppose that x is any number if it is added in infinity then it gives infinity.

Mathematical Form:

x+ ∞ = ∞

**Subtraction property of Infinity**

Suppose that x is any number if it is subtracted from infinity then it gives infinity or if infinity is subtracted form x it gives same result.

Mathematical Form:

x - ∞ = ∞

∞ - x= ∞

**Multiplication Property of Infinity:**

If any number x is multiplied by infinity, then it gives infinity.

**Mathematical Form:**

- If any number x is multiplied by infinity, then it gives infinity.

x. ∞ = ∞

- If infinity is multiplied by infinity, then infinity is answer as a result.

Mathematical Form:

- ∞. ∞ = ∞
- +∞ . -∞ = -∞
- (-∞) . (-∞) = ∞

**Quotient Property of infinity:**

- If any number x is divide by zero, then answer will be infinity as a result.

Mathematical Form:

x / 0 = ∞

- If infinity is divide by any number x then answer will be infinity as a result.

Mathematical Form:

∞ / 0 = ∞

- If infinity is divide by infinity, then answer will be infinity as a result.

Mathematical Form:

∞ /∞ = ∞

**Examples of Infinity:**

There are many examples of infinity some important are listed below:

**Set of Real Numbers:**

The set of real numbers are obtained by the union of rational and irrational numbers. The gap between two real numbers is infinite so real line is infinite.

**Repeated numbers refer to as infinity.**

If solve the factor 1 / 9 it gives 0.111111…. it means 1 repeated infinite time.

**Value of pi****π**.

The value of pi is continuing infinite times.

**The set of prime numbers.**

The prime numbers are endless.

**Infinite Sequence:**

The sequence form ½, 1/3, 1/4…. Is an infinite sequence.

**Applications of Infinity:**

There are many applications of infinity. Some discussed here,

**Infinity in Our Life:**

Despite the fact that our life on earth is limited but our souls are immortal. The infinite sign is utilized in meditation to remind us of equilibrium, balance, calm, and unity. We can theoretically reflect and approximate a valuation circumstance using the idea of infinity. Infinity can never be actual, described, or measured, hence the only way it can be used in real life is as a hypothetical, abstract idea to support a claim or provide evidence.

**Infinity in mathematics:**

When comparing the sizes of sets, such as the set of counting numbers, the set of real number points, and so on, the infinity symbol is used directly.

**Infinity in Physics:**

When one inquiry about the universe's eternal existence or the existence of an unlimited number of stars.

## Exponent Power Infinity

Exponent Power Infinity | Answer |
---|---|

e^∞ | ∞ |

e^-∞ | 0 |

e^∞+e^-∞ | ∞ |

e^-∞+e^-∞ | 0 |

## FAQs

**1. What is meant by infinity?**

The concept of infinity refers to something that has no beginning or end. It is generally something that has no restrictions. It is a condition in which there are no boundaries in regard to time, space, or any other kind of dimension.

** 2. Who was introduce the symbol of infinity?**

English mathematician John Wallis created the standard sign for infinity, in 1655. The term "infinity" in mathematics refers to something that is larger than a real number.

**3**. **Give some examples of infinity?**

**Set of Real Numbers:**

The set of real numbers are obtained by the union of rational and irrational numbers. The gap between two real numbers are infinite so real line is infinite.

**Repeated numbers refer to as infinity.**

If solve the factor 1 / 9 it gives 0.111111…. it means 1 repeated infinite time.

** 4. What is importance of infinity in our daily life?**

Despite the fact that our life on earth is limited but our souls are immortal. The infinite sign is utilized in meditation to remind us of equilibrium, balance, calm, and unity. We can theoretically reflect and approximate a valuation circumstance using the idea of infinity. Infinity can never be actual, described, or measured, hence the only way it can be used in real life is as a hypothetical, abstract idea to support a claim or provide evidence.

**5. What is importance of infinity in mathematics?**

When comparing the sizes of sets, such as the set of counting numbers, the set of real number points, and so on, the infinity symbol is used directly.

**References:**

Tapp, C., 2011. Infinity in mathematics and theology. *Theology and Science*, *9*(1), pp.91-100.

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*This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.*

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