Proof of 1=2

X=X Squaring X^2=X^2 Therefore X^2 -X ^2=0 (X+X)(X-X)=0 (By factorisation) Also X(X-X)=0 Or X+X=X 1=2

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.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered 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"

Math	Appears 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

There is no legitimate way to prove that $1=2$ . Do you know why? Because $1\neq 2$ .

On one point in your "proof", you divided by zero. You can't do that. Mathematics won't take responsibility for anything that happens after you divide by zero.

You could have saved yourself the trouble by writing $1\times 0=2\times 0$ and cancel out the zeros to get $1=2$ . But that is invalid. Any proof that allows division by zero isn't a proof at all.

Mursalin Habib - 7 years, 10 months ago

1 squared=1 2 squared=2+2 3squared=3+3+3 in the same way X squared= X+X+X+X+X+X+X+X+X+.......+X X times _{1} differentiate both sides of 1 with respect to X 2X=1+1+1+1+1+1+1+1+1+.............+1 X times i.e 2X=X therefore 2=1

A Former Brilliant Member - 7 years, 10 months ago

Notice that this argument is similar to this one.

So, what is wrong with your 'proof'?

Notice that your definition of $x^2$ is incomplete because it only works for positive integer values of $x$ . Graph it and you'll get points, not a line. Your function is not continuous. You can't even differentiate it.

What does the operator $\frac{d}{dx}$ do? It takes a function $f(x)$ and spits out a new function that tells you what the slope of $f(x)$ is for a particular $x$ .

If you want to find the slope of $f(x)$ for a particular $x$ graphically, what do you do?

You find the point $(x, f(x))$ and draw a straight line tangential to $f(x)$ at that point. Then you calculate $\tan \theta$ where $\theta$ is the angle our straight line makes with the positive $x$ axis.

Now let's get back to your problem. Do you remember that we had points scattered on the $xy$ plane? Let's find the slope of your defined function $x^2$ for a particular $x$ . Now how do we do that? Can you draw a line tangential to a point? Nope.

Moral: You can't differentiate discontinuous functions.

Mursalin Habib - 7 years, 10 months ago

@Mursalin Habib – yeah but y=x^2 is a continous problem

Abdhi Sharan - 6 years, 3 months ago

Math	Appears 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}`	$\boxed{123}$