What do you assume in an indirect proof

Do you really want to prove that by plugging in every conceivable combination of numbers? Here is a sampling:. You could spend every waking minute plugging in numbers without success. To solve this using an indirect proof, assume integers do exist that satisfy the equation. Then work the problem:. You see the contradiction? No; that is not possible. Indirect proof, or proof by contradiction, is yet another useful tool to help you with geometry.

Use it wisely it is not suitable for every problem , tell your reader or teacher you are using it, and work carefully. Get better grades with tutoring from top-rated professional tutors. Get help fast. Want to see the math tutors near you? Direct vs. Indirect Proof An indirect proof can be thought of as "the long way around" a problem. Here are the three steps to do an indirect proof: Assume that the statement is false Work hard to prove it is false until you bump into something that simply doesn't work, like a contradiction or a bit of unreality like having to make a statement that "all circles are triangles," for example If you find the contradiction to your attempt to prove falsity, then the opposite condition the original statement must be true First Step Of Indirect Proof Geometricians such as yourself can get hung up on the very first step, because you have to word your assumption of falsity carefully.

Most mathematicians do that by beginning their proof something like this: "Assuming for the sake of contradiction that …" "If we momentarily assume the statement is false …" "Let us suppose that the statement is false …" Aha, says the astute reader, we are in for an indirect proof, or a proof by contradiction. Indirect Proof Examples Here are three statements lending themselves to indirect proof.

The question to ask is, "What if that statement is not true? Quantifiers 3. De Morgan's Laws 4. Mixed Quantifiers 5. Logic and Sets 6. Families of Sets 2 Proofs 1. Direct Proofs 2. Divisibility 3. Existence proofs 4. Induction 5. Uniqueness Arguments 6. Indirect Proof 3 Number Theory 1. Congruence 2. The Euclidean Algorithm 4. The Fundamental Theorem of Arithmetic 6. The Chinese Remainder Theorem 8.

The Euler Phi Function 9. The Phi Function—Continued Wilson's Theorem and Euler's Theorem Public Key Cryptography Quadratic Reciprocity 4 Functions 1. Definition and Examples 2. Induced Set Functions 3. Injections and Surjections 4.

More Properties of Injections and Surjections 5. Varsity Tutors connects learners with experts. Instructors are independent contractors who tailor their services to each client, using their own style, methods and materials. Indirect Proof Proof by Contradiction To prove a theorem indirectly, you assume the hypothesis is false, and then arrive at a contradiction.

Example: Prove that there are an infinitely many prime numbers. Therefore, there are infinitely many primes. Subjects Near Me.