Basic Inequality Prove: $A\leq B\wedge B\leq A \Rightarrow A=B$

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In summary, the basic inequality prove A≤B∧B≤A states that if two numbers, A and B, are both less than or equal to each other, then they must be equal. This prove is important in mathematics as it establishes the concept of equality and can be used to solve more complex inequalities. It also has real-life applications, such as comparing quantities or determining if two objects have the same value. Additionally, this prove can be applied to variables other than numbers as long as they follow the same rules of inequality. Some possible extensions of this prove include exploring more complex inequalities and incorporating it into other mathematical concepts.
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solakis1
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Prove:

$A\leq B\wedge B\leq A\Rightarrow A=B$
 
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  • #2
Trichotomy: Given numbers A and B, one and only one must be true:
1) A> B
2) A< B
3) A= B

Since \(\displaystyle A\le B\), A> B is not true.
Since \(\displaystyle B\le A\), A< B is not true.
 
  • #3
Is the trichotomy law you are using Equivelant to the following:
$A<B\vee B<A\vee A=B$
 

FAQ: Basic Inequality Prove: $A\leq B\wedge B\leq A \Rightarrow A=B$

What does the basic inequality prove state?

The basic inequality prove states that if two numbers, A and B, are less than or equal to each other, then they must be equal.

How is this inequality proven?

This inequality is proven using the transitive property of equality, which states that if A=B and B=C, then A=C. In this case, A=B and B=A, so by transitivity, A=A, which means A=B.

What is the significance of this inequality?

This inequality is significant because it is a fundamental concept in mathematics and is used in many proofs and theorems. It also helps to establish the concept of equality and its properties.

Can this inequality be applied to other mathematical operations?

Yes, this inequality can be applied to other mathematical operations such as addition, subtraction, multiplication, and division. As long as the operations follow the same properties of transitivity, this inequality can be applied.

Are there any exceptions to this inequality?

No, there are no exceptions to this inequality. It holds true for all real numbers and cannot be disproven.

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