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

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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TopNewestI 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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$f(x)=x^2$ satisfies those properties.(It does not though)

I am not much familiar with "piece-wise" defined. But for instance , a function sayLog 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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Wha 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

$f(x)=x^2$, no? I don't see a formal definition of

Something likenon-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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