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The most beautiful solution ever!

First of all I want to say that this is not the namesake competition . We are not " you against me " but " infinity against infinity". This post is for all those who have either created or have perceived " the most beautiful solution ever " .I created this for the dreamers who may want to wander through the realms of mathematics in one alley having many shops . Please provide the link to that particular solution(s).

Note by Raven Herd
1 year, 12 months ago

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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} \( \boxed{123} \)

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Claim: An irrational raised to the power of an irrational can be a rational.

Proof: Either \(\sqrt{2}^\sqrt{2} \) is irrational or rational.

If it is rational, we are done.

Otherwise, \({\sqrt{2}^\sqrt{2}}^\sqrt{2} =\sqrt{2}^2 = 2 \) is rational.

Agnishom Chattopadhyay - 1 year, 11 months ago

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Nice example, but I think that the last equation should be written as

\(\large (\sqrt{2}^{\sqrt{2}})^{\sqrt{2}} = \sqrt{2}^{(\sqrt{2}\times \sqrt{2})} = \sqrt{2}^{2} = 2,\)

since \(\large \sqrt{2}^{\sqrt{2}^{\sqrt{2}}} = 1.7608.....\) is irrational.

Brian Charlesworth - 1 year, 11 months ago

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Nice : )

Raven Herd - 1 year, 11 months ago

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