How to prove irrational numbers?

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1. I have proved in earlier exercises of this book that $\sqrt 2$ and $\sqrt 3$ are irrational. Then, the sum of two irrational numbers is an irrational number. Thus

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2. In mathematics, an irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or

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3. Philosophically why should proving that $\gamma$ is irrational (let alone transcendental) be so much harder than proving $\pi$ or $e$ are irrational?

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4. Wrath, Actually, Sal was saying that there are an infinite number of irrational numbers. And there is at least one irrational number between any two rational numbers.