Problem 1.4. For x,y ∈ R def i ne x ∼ y to mean that x − y ∈ Z. 1)Prove that ∼ is an equivalence relation on R. 2)List three real numbers x such that x ∼ √2.

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Problem 1.4. For x,y ∈ R def i ne x ∼ y to mean that x − y ∈ Z. 1)Prove that ∼ is an equivalence relation on R. 2)List three real numbers x such that x ∼ √2.

Siddhant Zine 11th Nov, 2020

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priyaankasarkar Student Expert 13th Nov, 2020

If this is regarding Equivalence relations, we would suggest you to check the official page for lectures on Equivalence relations: http://www.cs.fsu.edu/~lacher/courses/MAD3105/lectures/s1_3equivrel.pdf . This is because there are few symbols, that might not be typed accurately here.

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