Less than is a mathematical symbol that represents an inequality between two numbers or expressions. It is typically used to compare two numbers or expressions and determine which one is smaller. The less than symbol is “<”.

Understanding Less Than

The less than symbol is used to compare two numbers or expressions and determine which one is smaller. For example, the expression “3 < 5” is true because 3 is less than 5. The expression “5 < 3” is false because 5 is not less than 3.

The less than symbol can also be used to compare expressions that are not numbers. For example, the expression “x < y” is true if x is less than y. The expression “x < y” is false if x is not less than y.

Properties of Less Than

The less than symbol has several properties that are important to understand. These properties include:

• Transitivity: If a < b and b < c, then a < c.
• Reflexivity: a < a is always false.
• Symmetry: If a < b, then b > a.
• Asymmetry: If a < b, then b > a.

Applications of Less Than

The less than symbol is used in a variety of applications, including:

• Mathematics: The less than symbol is used to compare numbers and expressions in mathematical equations and inequalities.
• Science: The less than symbol is used to compare measurements and data in scientific experiments and observations.
• Engineering: The less than symbol is used to compare specifications and tolerances in engineering design and construction.
• Finance: The less than symbol is used to compare prices, interest rates, and other financial data.

The less than symbol is a mathematical symbol that represents an inequality between two numbers or expressions. It is typically used to compare two numbers or expressions and determine which one is smaller. The less than symbol has several properties that are important to understand, and it is used in a variety of applications.

Symbol of Less Than

The symbol of less than is $<$. It is used to compare two values and indicate that the value on the left is less than the value on the right. For example, 3 < 5 means that 3 is less than 5.

Usage of the Symbol

The symbol of less than is used in a variety of mathematical contexts. It is used to compare numbers, variables, and expressions. It is also used to define inequalities and to represent the concept of a limit.

Comparing Numbers

The symbol of less than is used to compare two numbers and indicate that the value on the left is less than the value on the right. For example, 3 < 5 means that 3 is less than 5.

Comparing Variables

The symbol of less than can also be used to compare two variables. For example, if x and y are two variables, then x < y means that x is less than y.

Comparing Expressions

The symbol of less than can also be used to compare two expressions. For example, if x + 1 and y - 2 are two expressions, then x + 1 < y - 2 means that x + 1 is less than y - 2.

Defining Inequalities

The symbol of less than is used to define inequalities. An inequality is a mathematical statement that compares two values and indicates that they are not equal. For example, the inequality x < 5 means that x is not equal to 5 and that x is less than 5.

Representing the Concept of a Limit

The symbol of less than is also used to represent the concept of a limit. A limit is a value that a function approaches as the input value approaches a certain point. For example, the limit of the function f(x) = x^2 as x approaches 0 is 0. This means that as x gets closer and closer to 0, the value of f(x) gets closer and closer to 0.

The symbol of less than is a versatile mathematical symbol that is used in a variety of contexts. It is used to compare numbers, variables, and expressions. It is also used to define inequalities and to represent the concept of a limit.

Solved Examples of Less Than

Example 1: Comparing Two Numbers

Compare 5 and 3 using the less than operator.

5 < 3

The result of this comparison is $False$, because 5 is not less than 3.

Example 2: Comparing a Number to a Variable

Assign the value 10 to the variable $x$.

x = 10

Compare $x$ to the number 5 using the less than operator.

x < 5

The result of this comparison is $False$, because $x$ is not less than 5.

Example 3: Comparing Two Variables

Assign the value 7 to the variable $y$.

y = 7

Compare $x$ to $y$ using the less than operator.

x < y

The result of this comparison is $True$, because $x$ is less than $y$.

Example 4: Comparing a Number to a String

Compare the number 5 to the string $“10”$ using the less than operator.

5 < “10”

The result of this comparison is $True$, because the number 5 is less than the string $“10”$.

Example 5: Comparing Two Strings

Compare the string $“5”$ to the string $“10”$ using the less than operator.

“5” < “10”

The result of this comparison is $True$, because the string $“5”$ is less than the string $“10”$.

The less than operator can be used to compare two numbers, two variables, or a number and a string. The result of the comparison is a Boolean value, which is either $True$ or $False$.

Less Than FAQs

What is the difference between $<$ and $<=$?

The $<$ operator checks if the left operand is less than the right operand, while the $<=$ operator checks if the left operand is less than or equal to the right operand.

For example, the following expression will evaluate to $true$:

5 < 10

While the following expression will evaluate to $false$:

5 <= 10

What is the difference between $<$ and $>$?

The $<$ operator checks if the left operand is less than the right operand, while the $>$ operator checks if the left operand is greater than the right operand.

For example, the following expression will evaluate to $true$:

5 < 10

While the following expression will evaluate to $false$:

5 > 10

What is the difference between $<$ and $>=$?

The $<$ operator checks if the left operand is less than the right operand, while the $>=$ operator checks if the left operand is greater than or equal to the right operand.

For example, the following expression will evaluate to $true$:

5 < 10

While the following expression will evaluate to $false$:

5 >= 10

What is the difference between $<$ and $!=$?

The $<$ operator checks if the left operand is less than the right operand, while the $!=$ operator checks if the left operand is not equal to the right operand.

For example, the following expression will evaluate to $true$:

5 < 10

While the following expression will evaluate to $false$:

5 != 10

What is the difference between $<$ and $==$?

The $<$ operator checks if the left operand is less than the right operand, while the $==$ operator checks if the left operand is equal to the right operand.

For example, the following expression will evaluate to $true$:

5 < 10

While the following expression will evaluate to $false$:

5 == 10