05 Logic of Natural Numbers.pdf - The Logic of the Natural Numbers The natural numbers • most of you include counting addition and measurement among

05 Logic of Natural Numbers.pdf - The Logic of the Natural...

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The Logic of the Natural Numbers
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The natural numbers most of you include counting, addition, and measurement among the most elementary things you do. of all sets, the set of the natural numbers, = {0,1,2, …}, is the most elementary, yet has many mysterious properties. Among other things, it is our first encounter with infinity in this class. it comes with a new proof technique - mathematical induction. To prove something about an infinite set of numbers, we need a clever way to perform an infinite set of proofs - an infinite set of instances of the deduction theorem.
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The natural numbers most of you include counting, addition, and measurement among the most elementary things you do. of all sets, the set of the natural numbers, = {0,1,2, …}, is the most elementary, yet has many mysterious properties. Among other things, it is our first encounter with infinity in this class. it comes with a new proof technique - mathematical induction. To prove something about an infinite set of numbers, we need a clever way to perform an infinite set of proofs - an infinite set of instances of the deduction theorem. Stay tuned.
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Introduction to the Natural Numbers A Little Logic makes an e ff ort to provide a careful introduction to the Naturals, that shows, perhaps in too much detail (at least here and there) that the logic of numbers is just an extension of plain old logic. These slides give a slightly di ff erent, but hopefully consistent perspective First, we will take some time to get familiar with the basics
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Zero, and all the rest of the natural numbers We begin with a single number called zero, which we write as 0. The first number. (We hope.)
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