# 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
5 years, 5 months ago

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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?

- 5 years, 5 months ago

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

- 5 years, 5 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.

- 5 years, 5 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)

- 5 years, 5 months ago

I have rephrased the problem statement. I hope it does not cause any issue now.

- 5 years, 5 months ago

I realized that the rephrased statement is even more silly , I have again rephrased lol

- 5 years, 5 months ago

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

- 5 years, 5 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

- 5 years, 5 months ago

Correct.....

- 5 years, 5 months ago

Wha do you mean by not piecewise defined?

- 5 years, 5 months ago

This should be helpful.

- 5 years, 5 months ago

I know what piecewise means. What is an example of a function not piecewise?

- 5 years, 5 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.

- 5 years, 5 months ago

Haha, a better phrasing could be an elementary function, a function with a closed form, etc.

- 5 years, 5 months ago