Infinity- Concept, Meaning, Type & Symbol 

Lesson Overview

• What Is Infinity in Math?
• The Symbol of Infinity
• Adding, Subtracting, and Multiplying with Infinity
• Is Infinity a Number?
• Value of Infinity
• Solved Examples of Infinity
• Infinity Assessment

What Is Infinity in Math?

Infinity is a concept that means "without any end." It is not a specific number but something that keeps going forever. 

Imagine you are walking on a circular track. If you keep walking without stopping, you will keep going around the track endlessly. You can never reach an "end" because the circle has no starting or ending point.

In the same way, think about the sequence of numbers. Start counting from 1:
1, 2, 3, 4, 5, and so on.
No matter how high you count, there will always be a bigger number. You can never reach the "last number." This endless counting represents infinity in mathematics.

The Symbol of Infinity

The symbol of infinity is ∞. It looks like a sideways number eight. Mathematicians use this symbol to represent something that has no end. For example:

• In a number line, ∞ shows numbers going endlessly to the right.
• Negative ∞ (−∞) shows numbers going endlessly to the left.

Adding, Subtracting, and Multiplying with Infinity

When doing operations like addition, subtraction, and multiplication with infinity, we follow specific rules because infinity behaves differently.

Is Infinity a Number?

Infinity is not a number. It is an idea or concept that shows something without limits. Numbers are fixed and can be counted, but infinity keeps going.

Example:

Imagine you are filling a jar with marbles. If the jar had an infinite capacity, no matter how many marbles you add, the jar would never be full. This shows infinity is not a fixed number-it is an idea that something goes on forever.

Value of Infinity

Infinity does not have a value like regular numbers. It cannot be measured, and it never ends. 

For example, the value of numbers between 0 and 1 can be infinite because you can keep dividing the distance into smaller parts (like 0.1, 0.01, 0.001, and so on).

Take This Quiz :

Trivia Quiz: The Concept of Infinity

Solved Examples of Infinity

Here are some examples to help you understand how infinity works in math:

1. Infinite Series Example
   If you add numbers like 1 + 1/2 + 1/4 + 1/8 + ..., the sum gets closer to 2 but never actually reaches it. This shows how infinity works in an infinite series.
2. Dividing a Number by Infinity
   If you divide any number by infinity (e.g., 1 ÷ ∞), the result is 0 because the number becomes so small that it approaches zero.
3. Infinity in Limits
   In calculus, if you have a function like 1/x, as x becomes infinitely large, the value of 1/x approaches 0. This is written as:
   lim (x → ∞) 1/x = 0.
4. Adding Infinity
   Infinity + 5 = Infinity. Adding any finite number to infinity still gives infinity because infinity has no end.

Multiplying Infinity
Infinity × 2 = Infinity. Multiplying infinity by any number results in infinity because infinity cannot be increased in a measurable way.

Infinity Assessment

1. Identify whether the following statement is true or false:
   "Infinity is a number that has no end."
2. Fill in the blank:
   If you divide 1 by infinity, the result is ___.
3. Choose the correct answer:
   What symbol is used to represent infinity?
   a) ∞
   b) π
   c) √
   d) ≠
4. True or False:
   Infinity + 100 is still infinity.
5. Solve:
   What is the result of multiplying infinity by 2?
6. Explain briefly:
   Why is infinity not considered a specific number?
7. Fill in the blank:
   The series 1 + 1/2 + 1/4 + 1/8 + ... approaches the value ___.
8. True or False:
   Infinity can be reached by counting all the numbers.
9. Choose the correct answer:
   What happens to the value of 1/x as x approaches infinity?
   a) It becomes 0
   b) It becomes infinity
   c) It remains 1
   d) It becomes undefined

Write an example:
Provide one practical example of how infinity is used in mathematics.