What is meant by absurd in for

In mathematics, the term "absurd" is used to refer to a statement or proposition that is logically false or contradictory. It can also refer to a situation that is highly unlikely or unreasonable. In the context of a proof, an absurdity is often reached when a series of logical deductions leads to a contradiction, indicating that the original assumption or hypothesis was false.

For example, consider the following argument:

1. Assume that x = 1.

2. Multiply both sides of the equation by 2: 2x = 2.

3. Subtract x from both sides of the equation: 2x - x = 2 - x.

4. Simplify the left side: x = 2 - x.

5. Add x to both sides of the equation: 2x = 2.

6. Divide both sides of the equation by 2: x = 1.

This argument reaches an absurdity because it leads to the conclusion that x is both equal to 1 and equal to 2 - x, which is a contradiction. Therefore, the original assumption that x = 1 must be false.

In general, when an absurdity is reached in a proof, it indicates that there is an error in the reasoning or that the original hypothesis is not true. It can be a useful tool for identifying and correcting errors in logical arguments.