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# Better see your calendar first

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

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 $$400$$.
###### This problem is original

Note by Nihar Mahajan
1 year, 6 months ago

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Wha do you mean by not piecewise defined? · 1 year, 6 months ago

This should be helpful. · 1 year, 6 months ago

I know what piecewise means. What is an example of a function not piecewise? · 1 year, 6 months ago

Something like $$f(x)=x^2$$, no? I don't see a formal definition of non-piecewise anywhere, so I guess there's a scope for ambiguity. I can't do a better phrasing for a troll (not quite mathematical) problem. · 1 year, 6 months ago

Haha, a better phrasing could be an elementary function, a function with a closed form, etc. · 1 year, 6 months ago

Well , do you guys want me to reveal the answer? · 1 year, 6 months ago

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 · 1 year, 6 months ago

Correct..... · 1 year, 6 months ago

I do not understand the problem. We already have defined f in the problem statement. How can we improve upon that? · 1 year, 6 months ago

You have to find all f(x) which have those two properties. · 1 year, 6 months ago

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. · 1 year, 6 months ago

I realized that the rephrased statement is even more silly , I have again rephrased lol · 1 year, 6 months ago

I have rephrased the problem statement. I hope it does not cause any issue now. · 1 year, 6 months 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) · 1 year, 6 months ago