\[f\colon\Bbb Z\to\{28,29\}~,~ f(x)= \begin{cases} 29 \ \ \text{if} \ [x] \in \{[4k]\mid 0\leq k\leq 99~\land~k\notin\{25,50,75\}\} \ \\ 28 \ \text{otherwise} \end{cases} \]

Find a function \(g\colon\Bbb Z^+\cup\{0\}\to\{28,29\}\) which is not piece-wise defined and is identical to \(f\) in its own domain.

The function you should be seeking for might not be that mathematical....

**Clarifications:**

- \([x]\) denotes the congruence class of \(x\) modulo \(400\).

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## Comments

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TopNewestWha do you mean by not piecewise defined?

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This should be helpful.

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I know what

piecewisemeans. What is an example of a functionnotpiecewise?Log in to reply

non-piecewiseanywhere, so I guess there's a scope for ambiguity. I can't do a better phrasing for a troll (not quite mathematical) problem.Log in to reply

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Well , do you guys want me to reveal the answer?

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I think the question you're really trying to as is "What is f better known as"?

The answer to that is f(x) is the number of days in the february of year x

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Correct.....

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I do not understand the problem. We already have defined f in the problem statement. How can we improve upon that?

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You have to find all f(x) which have those two properties.

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I think you mean a function \(f(x)\) which satisfies those two properties but is not piecewise defined?

The problem, as is currently phrased, doesn't make sense since we already have that \(f(x)\), piecewise defined! You don't find stuff that suits a definition, you define stuff and go from there.

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