# Math Proof

Prove: let alpha be a lower bound of a subset E of an ordered set S. If alpha exist in E, then alpha= infE(greatest lower bound of E).

PF: Already have alpha is a lower bound of E. Let lambda be a different lower bound of E. If alpha precedes lambda, the lambda will not be a lower bound because alpha exist in E. So, lambda precedes alpha. Hence alpha=infE.

1. 👍 0
2. 👎 0
3. 👁 97

## Similar Questions

1. ### Calculus

Which of the following integrals correctly computes the volume formed when the region bounded by the curves x^2 + y^2 = 25, x = 4 and y = 0 is rotated around the y-axis? A. pi ∫ upper bound of 3 and lower bound of 0 ( sqrt(25 -

asked by Justin on June 24, 2019
2. ### algebra

Let D = {(a,b,2a): a,b all real numbers} The set of vectors in R^3 with last entry twice the first. E = span{(1,0,2),(2,-1,4),(0,-3,0)} Prove that D = E I first made an augmented matrix to find out that there is a free variable of

asked by Daniel on June 7, 2013
3. ### Discrete Math

For sets A, B, C is a subset of U, prove or disprove (with a counter-example) the following: If A is a subset of B, B is not a subset of C, then A is not a subset of C,

asked by Ron on April 5, 2013
4. ### smallest algebra

Let F be a family of subsets of a set X such that empty set is the element of F. A subset A of X belongs to F1 if and only if either A is a subset of F or complement of A is the subset of F. A subset B of X belongs to F2 if and

asked by sxxx123456 on January 15, 2009
5. ### math

Rewrite the following using mathematical symbols: a. Q is equal to the set whose elements are a, b, and c. b. The set containing 1 and 3 only is a proper subset of the set of natural numbers. c. The set containing 1 and 3 only is

asked by susan on August 18, 2012
6. ### math

Let f:A->B, where A and B are nonempty, and let T1 and T2 be subsets of B. a.Prove that f^-1(T1 U T2)= f^-1(T1) U f^-1(T2). b.Prove that f^-1(T1 intersects T2) = f^-1(T1) intersects f^-1(T2). I think once I see a I can do b. c.

asked by dreww1961 on October 14, 2010
7. ### Set Thoery

(1)Given the sets A={a,b}, B={a,b,c}, C= {b,c,d}. which of these sets are: (i) Equal (ii) Comparable (iii) Subset (2) Prove that if A is a subset of B and B is a subset of C then A is a subset of C

asked by Matrix School 2 on July 14, 2009
8. ### Chebyshev's Theorem

What is difference between taking the lower bound and lower limit from Chebyshev's Theorem? If P(|Y- mean|)

asked by Aryaa on December 2, 2019