Help Me! Functions, limits and continuity

Hey guys,

Today I came across a question about the function f(x)f(x), which takes the value xx when xQx \in Q and the value 1x1-x when xQx \notin Q. Is this function continuous at any point?

I thought that f(x)f(x) would be continuous at x=0.5x=0.5 since the left and right hand limits seem to approach 0.50.5 near x=0.5x=0.5.

Am I correct? If so, why? If not, why?

Thanks!

Note by Raj Magesh
4 years, 4 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

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 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

Do you know what is the delta epsilon definition of a limit?

Calvin Lin Staff - 4 years, 4 months ago

Log in to reply

Thanks a lot! I went through the wiki and worked out the answer to my question. The epsilon-delta definition is broader than the one I learnt in school...

Raj Magesh - 4 years, 4 months ago

Log in to reply

hi

Lucy Oakley - 3 years, 11 months ago

Log in to reply

Hey.

Raj Magesh - 3 years, 10 months ago

Log in to reply

How are you

Lucy Oakley - 3 years, 10 months ago

Log in to reply

@Lucy Oakley Great, you?

Raj Magesh - 3 years, 10 months ago

Log in to reply

These are called drichlet functions and these are continuos when both equations are equal

Harshita Arya - 4 years, 4 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...