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# Wiki on Functional Equations:substitution

Hey guys,I have just contributed to this wiki .The wiki is far from complete.I will appreciate any sort of feedback.

I realize that there are many typos.If you see a typo that is annoying you,just edit it without asking(unless you are having doubts).The math formatting could use some help.I intentionally did not align brackets,because they take a lot of work.

Thanks in advance.

Note by Rahul Saha
3 years, 1 month ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. 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 1paragraph 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

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This is great! I like that you split it out into cyclic functions, and functions of 2 variables, as those are 2 distinct cases.

I think that there should be an initial section where the problems are similar to the first example, and it's just "replace x+3 with y, to find the equation". I see that you referenced the "Functional Equations - Introduction" wiki which explains them in detail. We will either merge these two pages together, or edit it to make the formatting more obvious. These problems can be hard to resolve easily, for someone that is new to it. It's also considered a basic approach in functions, but not often explained well.

I'm really excited to see more functional equations pages developed. This was one topic that I really liked when doing olympiad problems, as it often highlighted creativity and finding suitable substitutions.

Staff - 3 years, 1 month ago

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Thanks for the feedback.I think that for those who intend to read these pages simply to refine their knowledge or something like that,the first problems won't bother them.But to those new,I believe you have a great point which I unfortunately overlooked.Btw,I am against merging the two pages together.It is my experience that the longer the page seems to be,the more discouraged a person will become to actually read anything on the page.I guess formatting the page is the better solution here.I hope someone(perhaps me) will add more basic problems.For the record,I had a tough time resolving these basic issues as well.

Again,thanks for the feedback.

- 3 years, 1 month ago

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@Rahul Saha this is great! Thanks! I'm going to do some minor edits right now, but this is a great contribution.

Staff - 3 years, 1 month ago

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