- #31
johnqwertyful
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NATURE.M said:
No more than you need to justify n+1>n.
Explaining Why 1.1 and 0.95 Are Not Least Upper Bounds for Set A
- Thread starter NATURE.M
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The discussion centers on proving that 1.1 and 0.95 are not the least upper bounds (lub) for the set A, which consists of numbers in the form n/(n+1) for positive integers n. It is established that 1.1 cannot be the lub because there exist upper bounds less than 1.1, such as 1.01, contradicting the definition of the least upper bound. Similarly, 0.95 is shown not to be the lub since there are numbers in A greater than 0.95, specifically 1/2, which disqualifies it as an upper bound. The conversation emphasizes the importance of concise proofs and the correct application of the least upper bound axiom. Ultimately, the correct least upper bound for set A is determined to be 1.
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