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(15) (a) State what it means to say that S has a least element. (b) Suppose that S does not have a least element. Show that for any x E S, there exists y ES such that y < x. (c) Let S be a subset of N such that S does not have a least element. Prove by complete induction that for every n E N, n & S. (d) Deduce that every nonempty subset of N has a least element.

(15) (a) State what it means to say that S has a least element. (b) Suppose that S does not have a least element. Show that for any x E S, there exists y ES such that y < x. (c) Let S be a subset of N such that S does not have a least element. Prove by complete induction that for every n E N, n & S. (d) Deduce that every nonempty subset of N has a least element.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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(15) (a) State what it means to say that S has a least element. (b) Suppose that S does not have a least element. Show that for any x E S, there exists y ES such that y < x. (c) Let S be a subset of N such that S does not have a least element. Prove by complete induction that for every n E N, n S. (d) Deduce that every nonempty subset of N has a least element.
Transcribed Image Text:(15) (a) State what it means to say that S has a least element. (b) Suppose that S does not have a least element. Show that for any x E S, there exists y ES such that y < x. (c) Let S be a subset of N such that S does not have a least element. Prove by complete induction that for every n E N, n S. (d) Deduce that every nonempty subset of N has a least element.
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