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My highschool teacher has informally told us about what continuity is and used step functions as an example of a discontinuous function.

The Wikipedia page for it links to a lot of other kind of step functions, such as the Heaviside step function.

What are some uses of these step functions to mathematicians at higher levels (or even in highschool)?

Irregular User
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Cathe1974
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2 Answers2

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Step functions can be used in the process of defining the Riemann integral, and in general for approximating continuous functions.

Chill2Macht
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    You can generalise even further to regulated functions, which continuous functions are a subset of. – Irregular User Apr 26 '16 at 21:46
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    Haha I learned something new today too! – Chill2Macht Apr 26 '16 at 21:47
  • @IrregularUser: What are "regulated functions", please? It is the first time that I encounter this term. – Alex M. Apr 28 '16 at 17:56
  • @AlexM. Here you go: https://en.wikipedia.org/wiki/Regulated_function I realise that this isn't exactly detailed, but perhaps it should give you a good idea? If you have further questions I'll be more than happy to answer them to the best of my ability :) – Irregular User Apr 28 '16 at 18:29
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Two of the most frequently used step functions are the "floor" and "ceiling" functions.

The floor function takes a real number and returns the largest integer(whole) number less then or equal the real number. For a positive real number this is equivalent to cutting off all the numbers after the decimal place.

The ceiling function returns the smallest integer number greater then the number given.

They are useful in rounding off and often arise in cases where there is some sort of calculation that results in a real number but only the whole part is meaningful.

Q the Platypus
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