# Real Analysis Proof: Prove mn=1 => m=1 & n=1 or m=-1 & n=-1

• johnjuwax
In summary, Real Analysis is a branch of mathematics that focuses on the study of real numbers and their properties, using rigorous proofs to establish the truth of mathematical statements. A proof in Real Analysis is a logical argument that starts with known axioms and uses logical reasoning and mathematical tools to arrive at a conclusion. The proof of mn=1 => m=1 & n=1 or m=-1 & n=-1 in Real Analysis is important because it shows the unique properties of real numbers and their relationship to multiplication, and it demonstrates the use of logical reasoning and axioms in proving mathematical statements. This proof can also be applied in other areas of mathematics, such as abstract algebra and number theory, to prove theorems and propositions related to multiplication
johnjuwax
Prove or disprove that if m and n are integers such that mn = 1 then either m= 1 & n = 1 or else m = -1 & n = -1.

What have you already tried and where are you stuck?

Petek

Have you tried to find any counterexamples? Usually that will either disprove the statement or give you a reason why no such counterexamples exist.

## 1. What is Real Analysis?

Real Analysis is a branch of mathematics that deals with the study of real numbers and their properties. It involves the use of rigorous mathematical proofs to establish the truth of mathematical statements.

## 2. What is a proof in Real Analysis?

A proof in Real Analysis is a logical argument that demonstrates the validity of a mathematical statement. It involves starting with known axioms and using logical reasoning and mathematical tools to arrive at a conclusion.

## 3. How do you prove mn=1 => m=1 & n=1 or m=-1 & n=-1 in Real Analysis?

To prove this statement, we can use the fact that the product of two real numbers is 1 if and only if both numbers are either 1 or -1. We can assume that mn=1 and then use the definition of equality to show that m=1 and n=1 or m=-1 and n=-1. We can also use proof by contradiction to show that if m and n are not both 1 or -1, then their product cannot equal 1.

## 4. Why is this proof important in Real Analysis?

This proof is important because it shows the unique properties of the real numbers and their relationship to multiplication. It also demonstrates the use of logical reasoning and axioms to prove mathematical statements, which is a fundamental concept in Real Analysis.

## 5. How can this proof be applied in other areas of mathematics?

This proof can be applied in other areas of mathematics, such as abstract algebra and number theory, where the properties of real numbers and multiplication are used extensively. It can also be used to prove other theorems and propositions that involve the concept of multiplication and equality.

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