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The Road to Reality Study Notes: Difference between revisions
→6.1 What makes an honest function?
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=== 6.1 What makes an honest function? === | === 6.1 What makes an honest function? === | ||
Calculus is built from the two ingredients, [https://en.wikipedia.org/wiki/Derivative differentiation] and [https://en.wikipedia.org/wiki/Integral integration]. Differentiation is a local phenomenon which concerns the rates that things change whereby integration is a more quantity that measures the totality. Incredibly, these two ingredients are the inverse of one another ([https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus fundamental theorem of calculus]). | |||
These two operate on ‘functions’ and Penrose notes that these can be thought of as ‘mappings’ from some array of numbers (domain) to another (target). Penrose gives the three examples below which will be used later in the chapter as mapping the real number system to itself: | |||
[[File:Fig 6p2.png|thumb]] | |||
=== 6.2 Slopes of functions === | === 6.2 Slopes of functions === | ||