Real Number System 1. Prove that in an ordered field 1> 0. Hint: First show that

Question

Real Number System 1. Prove that in an ordered field 1> 0. Hint: First show that a 0 if and only if 1 >0. Then show that (-z)2 2. Prove that ifx, y E R then | |xl-lyll lx-yl (you may use the triangle inequality) 3. Prove that an ordered set with the least upper bound property also has the greatest lower bound property 4. Prove that Q with the usual ordering does not have the least upper bound property. 5. Let A = {re R : x22). Prove that A is bounded from above and that if y = sup(A), then y2 2 in fact, y 2 but you don't need to show this)

Explanation / Answer

1.

Lets consider 1 <0

If 1<0 , if and only if -1>0

Here we got : -1>0

1 = (-1).(-1)

1 = (-1)2

hence (-1)2>0 ; 1>0 its contradiction is true.

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.