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Im currently writing an assignment in my math class. I have to calculate the amount of money an individual pays in taxes, based on his income.

Where I live (Denmark), if you earn more than 500.000DKK you will be charged an additional 7% in taxes for all money made above the 500.000DKK, and the regular 35%, for the rest. (Not actual numbers)

This is the best I could express the formula using my high school math:

MoneyIPayOf(income) = (income <= 500.000) ? (income * 0.35) : (500.000 * 0.35 + (income - 500.000) * 0.42)

Even I can see this formula makes no sense, but I have no idea how to formulate it in math, without the silly looking and programming inspired conditional statement.

How I hope people would read it is:

MoneyIPayOf(600.000) = (600.000 <= 500.000) : (500.000 * 0.35 + (600.000 - 500.000) * 0.42)

MoneyIPayOf(400.000) = (400.000 <= 500.000) : (400.000 * 0.35)

How could I write this formula properly, so real mathmaticians could understand it?

Cortex
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1 Answers1

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You could try to use something like max{(income - 500.000), 0} if you want an expression without an explicit conditional. Thus, when the income is lower than $500.00$, this term evaluates to $0$, which will not change the amount of the second case.

Anyways, mathematicians are used to conditional statements. You could write something like

$\text{MoneyIPayOf(income)}=\begin{cases}\text{formula 1} & \text{if income}\leq 500.000\\\text{formula 2}&\text{if income}\geq 500.000\end{cases}$

Babelfish
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  • The { operator is what i was looking for. For some reason I was unable to find it, what is that operator called? – Cortex May 16 '19 at 13:05
  • In Latex-code you use the cases environment: \begin{cases} formula1 & case1 \\ formula2 & case2\end{cases}. I don't think there is an official name, I would speak of a "case-distinction". – Babelfish May 16 '19 at 13:11