The Proof of the Cancellation Law of Addition

In the preceding posts, I have discussed the Axioms of Real Numbers and the Axioms of Equality. We will use these axioms to prove several basic theorems in Algebra. In this post, we prove the cancellation law of addition. That is, for any numbers a, b, and c,  if a + c = b + […]
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A Proof that Square Root of 2 Plus Square Root of 3 is Irrational

Introduction In the previous post, we have learned that is irrational.  In this post, we will use that theorem to show that is also irrational. This proof was explained by Ivan Niven in his book Numbers: Rational and Irrational. A common argument that might arise is that since is irrational and is irrational, then their […]
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Proof that Square Root of 6 is Irrational

Introduction We have learned that is irrational and thousands of sites on the internet will show you the proof that is irrational. In this post, we show that is irrational. This is a prerequisite for the next post which will show that is irrational. You will probably argue that since is irrational and is irrational, […]
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