# 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
2 years, 11 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

• bulleted
• list

1. numbered
2. list

1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

> This is a quote
This is a quote
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

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

Staff - 2 years, 11 months ago

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

- 2 years, 11 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.

- 2 years, 11 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)

- 2 years, 11 months ago

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

- 2 years, 11 months ago

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

- 2 years, 11 months ago

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

- 2 years, 11 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

Staff - 2 years, 11 months ago

Correct.....

- 2 years, 11 months ago

Wha do you mean by not piecewise defined?

Staff - 2 years, 11 months ago

- 2 years, 11 months ago

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

Staff - 2 years, 11 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.

- 2 years, 11 months ago

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

Staff - 2 years, 11 months ago