A lot of students have asked me in the past about proofs, and about how scared they are of them. To be totally honest with you, when I was an undergraduate, I was initially terrified of proofs! I thought that it was some sort of wizard skill that couldn’t be learned. The interesting thing is that, for a lot of higher-math (modern algebra, modern analysis, number theory), the actual math you will use to solve the proofs is very basic! In this exercise, we prove that the square root of 3 is an irrational number. We use a 'Proof by Contradiction' and assume that the square root of 3 is actually a rational number, and we set it up as (sqrt)3 = a/b. We understand that a and b have to be integers, that they have to have a greatest common divisor of 1 (in other words, they can’t be reduced any further), and b cannot be 0. From there, we square both sides and perform some basic algebraic operations to discover that a^2 = 3b^2… which we discover means that 3 divides a. A bit later, we discover a similar truth about b… 3 divides b! Realizing that 3 divides both a and b, we can see that the greatest common divisor (gcd) is greater than one… and we have our contradiction! This is a fun proof that can really introduce you to the creativity that exists in mathematics beyond the rote memorization to which you may have grown accustomed.

-- From Augie K., Number Theory tutor on Chegg Tutors

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Number Theory tutoring on Chegg Tutors

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-- From Augie K., Number Theory tutor on Chegg Tutors

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Number Theory tutoring on Chegg Tutors

Learn how to solve proofs by contradiction on Chegg Tutors. Work with live, online Number Theory tutors like Augie K. who can help you at any moment, whether at 2pm or 2am.

Liked the video tutorial? Schedule lessons on-demand or schedule weekly tutoring in advance with tutors like Augie K.

Visit https://www.chegg.com/tutors/Number-Theory-online-tutoring/?utm_source=youtube&utm_medium=video&utm_content=managed&utm_campaign=videotutorials

----------

Like what you see? Subscribe to Chegg's Youtube Channel:

http://bit.ly/1PwMn3k

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Visit Chegg.com for purchasing or renting textbooks, getting homework help, finding an online tutor, applying for scholarships and internships, discovering colleges, and more!

https://chegg.com

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Want more from Chegg? Follow Chegg on social media:

http://instagram.com/chegg

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- Category
- number theory Mahematics
- Tags
- number theory, math

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