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Sample text

And following the usual conventions of mathematics we will ➝ ✶ ❂ give these variables short names constructed from lower case letters, for example, , , or ✳★✫ ✶ ✫✄✭✠✥❅✮✢✜ . We will also always declare the type of the variable, for example, ❫ ❲ indicates ✶ that the variable will stand for a person and not a sport or a number. This “typing" is just ✥❈❇✬✫ what we do with a word such as which can only ever stand for a feminine person or ✹✁❇✬✫✄✩ thing and a word such as which can only ever refer to a set of things.

A function ✛✄✼✯✫ is a single-valued fact about something. The notation tries to indicate that when the function is applied to some person then we will be led or pointed to one particular number. This is written as, for example: ✛✄✼✬✫ ✙✎✚✁✛✢✜☛❬ ➆ ✦★✧ ❱ ✛✄✼✬✫ ✙✎✚✁✛✢✜ The function symbol is written next to its argument, in this case, . The equality ✣✄✥ ➆ symbol corresponds to the word . 3. The underlying data is exactly the same, so why should we choose one style of declaration rather than the other?

2 Partial Functions Whenever we have the possibility of an incomplete functional relationship, we have a ❇✬✫✸✣❈✼✁❇✯✹ partial function. We might have a partial function. ❇✎✫✸✣❈✼✄❇✯✹ ❫ ❲ ✫✢✭✠✥✢✮✢✜ ➍➎ ❞❝ ❚ Everybody has just one height, so it is a functional relationship, but if we do not know every person’s height, or cannot guarantee that we will know, then the function is partial. The symbol for a partial function is ➍➎ ❜❝ which is similar to the ❜ ❞❝ symbol used for total functions but with a vertical bar.

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