sterilization
发表于 2025-3-25 03:53:50
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名字的误用
发表于 2025-3-25 10:44:31
https://doi.org/10.1007/978-3-663-04632-5In Chap. 12 we studied universal statements of the form . for given sets . and predicates .. Here we continue this discussion by examining the case when . is the set of natural numbers.
不来
发表于 2025-3-25 12:38:23
Unsymmetrische Bewegungsgesetze,In this chapter we discuss three variations of induction: strong induction, split induction, and double induction. This arsenal of induction techniques will allow us to prove a variety of fundamental and powerful mathematical statements.
Omnipotent
发表于 2025-3-25 17:30:25
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知道
发表于 2025-3-25 23:29:20
How to Make a Statement?In the previous chapter we learned how to introduce mathematical concepts with definitions or as primitives. Once we introduce a new concept, we are interested in its properties, usually stated as mathematical statements. . are sentences that are either true or false—but not both.
充满人
发表于 2025-3-26 03:17:30
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amyloid
发表于 2025-3-26 07:53:00
Recent Progress in MathematicsIn the last chapter we discussed seven of the most famous classical theorems of mathematics. We now turn to three more recent results to complete our top ten list. We will not provide any proofs—in fact, there are very (very!) few people who have seen complete proofs for these results.
防御
发表于 2025-3-26 11:02:40
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reserve
发表于 2025-3-26 12:45:46
Quantifier MechanicsWe introduced abstract mathematics in Chap. 1 with . games; in particular, we analyzed one such game, the .. Here we review this rather simple game as it will enable us to discuss quantifiers in a simple and natural way. Consider the following figure:
hypotension
发表于 2025-3-26 19:34:18
Mathematical StructuresIn Chap. 8 we made the somewhat heuristic claim that properties and identities about statements can easily be altered so that they also hold true for sets. As an example, we considered the claim that . holds for all statements ., ., and ..