Combining Texts
Ideas for
'Thinking About Mathematics', 'Philosophy of Mathematics' and 'On the Source of Necessity'
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6 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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10201
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Virtually all of mathematics can be modeled in set theory [Shapiro]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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8763
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The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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10213
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Real numbers are thought of as either Cauchy sequences or Dedekind cuts [Shapiro]
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18243
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Understanding the real-number structure is knowing usage of the axiomatic language of analysis [Shapiro]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
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18249
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Cauchy gave a formal definition of a converging sequence. [Shapiro]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
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18245
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Cuts are made by the smallest upper or largest lower number, some of them not rational [Shapiro]
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