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, 8 months ago

No vote yet
1 vote

  Easy Math Editor

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

[example link](https://brilliant.org)example link
> 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} \( \boxed{123} \)

Comments

Sort by:

Top Newest

Wha do you mean by not piecewise defined?

Agnishom Chattopadhyay Staff - 2 years, 8 months ago

Log in to reply

This should be helpful.

Prasun Biswas - 2 years, 8 months ago

Log in to reply

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

Agnishom Chattopadhyay Staff - 2 years, 8 months ago

Log in to reply

@Agnishom Chattopadhyay 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.

Prasun Biswas - 2 years, 8 months ago

Log in to reply

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

Agnishom Chattopadhyay Staff - 2 years, 8 months ago

Log in to reply

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

Nihar Mahajan - 2 years, 8 months ago

Log in to reply

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

Agnishom Chattopadhyay Staff - 2 years, 8 months ago

Log in to reply

Correct.....

Nihar Mahajan - 2 years, 8 months ago

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 Staff - 2 years, 8 months ago

Log in to reply

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

Nihar Mahajan - 2 years, 8 months ago

Log in to reply

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.

Prasun Biswas - 2 years, 8 months ago

Log in to reply

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

Nihar Mahajan - 2 years, 8 months ago

Log in to reply

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

Nihar Mahajan - 2 years, 8 months ago

Log in to reply

@Prasun Biswas 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)

Nihar Mahajan - 2 years, 8 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...