INDIRECT PROOF Meaning and
Definition
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Indirect proof, also referred to as proof by contradiction or reductio ad absurdum, is a logical method used in mathematics and logic to establish the truth of a statement indirectly. It involves assuming the opposite of what is to be proven and then demonstrating that this assumption leads to a contradiction or an absurdity. By showing that the opposite leads to an impossibility, it can be inferred that the original statement must, therefore, be true.
The process of an indirect proof typically involves a series of logical steps and reasoning. To begin, one assumes the opposite of what is to be proven, often called the negation of the statement. Then, logical deductions are made based on this assumption and the known principles and properties of the subject at hand. If, at any point, a contradiction or absurdity is reached, a statement that contradicts a known truth or a situation that defies common sense, then the original assumption must be false.
The strength of an indirect proof lies in its ability to establish the truth of a statement without directly proving it. It employs a form of reasoning that disallows the possibility of the opposite being true. This method is often used when direct proof methods are challenging or impossible to apply. Indirect proofs can lead to elegant, concise arguments and are commonly utilized in various branches of mathematics, such as geometry and number theory.
Common Misspellings for INDIRECT PROOF
- undirect proof
- jndirect proof
- kndirect proof
- ondirect proof
- 9ndirect proof
- 8ndirect proof
- ibdirect proof
- imdirect proof
- ijdirect proof
- ihdirect proof
- insirect proof
- inxirect proof
- incirect proof
- infirect proof
- inrirect proof
- ineirect proof
- indurect proof
- indjrect proof
- indkrect proof
- indorect proof
Etymology of INDIRECT PROOF
The term "indirect proof" is derived from two sources: "indirect" and "proof".
The word "indirect" comes from the Latin word "indirectus", which is a combination of "in" (meaning "not" or "against") and "directus" (meaning "straight" or "direct"). This Latin root conveys the idea of something being done in a roundabout or circuitous manner.
The word "proof" also has Latin roots, originating from the Latin word "probare", meaning "to test" or "to prove". It developed through Old French into Middle English with the same meaning.
When these two terms are combined, "indirect proof" refers to a method of proving a proposition or statement through a roundabout or alternative approach, rather than through a straightforward or direct demonstration.
