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

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 \(400\).

## Comments

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TopNewestWha do you mean by not piecewise defined? – Agnishom Chattopadhyay · 7 months, 3 weeks ago

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This should be helpful. – Prasun Biswas · 7 months, 3 weeks ago

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piecewisemeans. What is an example of a functionnotpiecewise? – Agnishom Chattopadhyay · 7 months, 3 weeks agoLog 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. – Prasun Biswas · 7 months, 3 weeks agoLog in to reply

– Agnishom Chattopadhyay · 7 months, 3 weeks ago

Haha, a better phrasing could be an elementary function, a function with a closed form, etc.Log in to reply

Well , do you guys want me to reveal the answer? – Nihar Mahajan · 7 months, 3 weeks ago

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The answer to that is f(x) is the number of days in the february of year x – Agnishom Chattopadhyay · 7 months, 3 weeks ago

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– Nihar Mahajan · 7 months, 3 weeks ago

Correct.....Log in to reply

I do not understand the problem. We already have defined f in the problem statement. How can we improve upon that? – Agnishom Chattopadhyay · 7 months, 3 weeks ago

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– Nihar Mahajan · 7 months, 3 weeks ago

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

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. – Prasun Biswas · 7 months, 3 weeks ago

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– Nihar Mahajan · 7 months, 3 weeks ago

I realized that the rephrased statement is even more silly , I have again rephrased lolLog in to reply

– Nihar Mahajan · 7 months, 3 weeks ago

I have rephrased the problem statement. I hope it does not cause any issue now.Log in to reply

– Nihar Mahajan · 7 months, 3 weeks ago

I am not much familiar with "piece-wise" defined. But for instance , a function say \(f(x)=x^2\) satisfies those properties.(It does not though)Log in to reply