## I can prove 2 = 1! Therefore algebra is false!

06 Nov

What if I told you that I could prove that 2 = 1, rendering all of algebra false and meaningless? Check out the work below:

Isn’t that undeniable? Clearly, you can see that by using algebra against itself, I have just proven algebra to be unreliable, because it can give us nonsensical results!

Eh? What’s that you say? Because a = b, that means that a β b = 0, and we can’t divide by zero (a β b)? Therefore I did it wrong?

Can you see where I’m going with this? I’m using the same tactic that creationists use in arguing against evolution, i.e. using what they think are actual claims regarding evolution (or made by the theory of evolution) in order to disprove evolution itself. Or, in general, just using straw-men arguments against evolution and “doing the work wrong”. Somewhere along the line, they fallaciously argue against evolution by making some claim that is either (1) provably false, or (2) something that does not invalidate evolution.

For instance, let’s take the common creationist argument that no case of macro-evolution has ever been observed. Oh, sure, micro-evolution has been observed, and is perfectly acceptable to the more intelligent creationists (and no, that’s not an oxymoron… I don’t think), but macro-evolution? Poppycock! Balderdash! Creationism is always the way!

What they fail to understand is that macro-evolution is simply micro-evolution on a much larger scale, and that if we ever observed one species changing into another over the course of just a few generations, then that would actually disprove evolution. We have yet to find any evidence against evolution. Evolution, like all scientific theories, allows us to make testable predictions about what one would expect to see in related areas. For example, since humans have 23 pairs of chromosomes and apes have 24, scientists predicted that somewhere along the line the fusion of two separate human chromosomes occurred. When we finally went to check, guess what we found?

So when a creationist tries to use fallacious reasoning in order to argue against evolution, instead of using science to disprove the theory, just imagine them committing a horribly wrong error in an algebra problem that ends up showing that 2 somehow equals 1 β it’s not that algebra itself is wrong; it’s their work and thought processes that are wrong.

1. August 29, 2012 at 7:03 pm

b = 0, a = 0

2b = b if b = 0

2. April 30, 2014 at 2:25 pm

lines 3 LHS does not equal line 4 LHS. Only exception is when ab-ba=0, but that will mess the rest of your equations.
http://en.wikipedia.org/wiki/Difference_of_two_squares

3. June 28, 2014 at 1:33 am

2b = b does not prove that 2 = 1.
2b = b therefore: 1. 2b – b = 0,
2. 2b – b = b,
3. b = 0
4. 2b = b = 0.

4. June 28, 2014 at 1:34 am

2b = b does not prove that 2 = 1, it proves that 0 = 0.

5. December 24, 2014 at 4:26 am

sorry bro,i cant accept your solving method and algebra is correct always,
problem is,in second line,
if , a=b then a^2!=ab its a^2=b^2

6. February 9, 2015 at 10:23 pm

First off, to everyone who has commented here, this ‘solution’ is completely correct with the ONE EXCEPTION that you can’t decide by 0. If you divide 2b=b by b, you get 2=1 (for bβ 0, obviously). And, besides that, the point of this article, which I must say is surprisingly well-written and succinctly put, IS EXACTLY THAT. You can prove anything (e.g. Creationism) if you use fallacious proofs. To go along with this, here’s a link for the full debate between Bill Nye (The Science Guy) and Ken Ham (CEO of Young Earth creationist (YEC) ministry Answers in Genesis (AiG)), with the topic “Is Creation A Viable Model of Origins?”. I’ve watched the entire thing, and it’s a really great debate. Ken Ham is surprisingly well spoken, and outdid my expectations. Take a look. https://m.youtube.com/watch?v=z6kgvhG3AkI

7. February 9, 2015 at 10:41 pm

Also, in response to Kiran, line 3 DOES equal line 4. ab-b^2=b(a-b) because you factor out the b (this is true for all values of b and/or a) and b^2-a^2=(b+a)(b-a). Its a basic Algebra 1 property. If you want proof distribute: b*b-ba+ab-a^2 which reduces to b^2-a^2. Their comment that it only works if ba-ab=0… WHICH IT ALWAYS DOES. Basic commutative property, ab=ba.

8. March 9, 2015 at 6:53 pm

bruh you’re retarded

9. March 20, 2015 at 4:57 pm

The error lies in dividing each side by (a-b). In this equation (a-b) cleary equals zero, so dividing by (a-b) makes lines five onward undefined. The result that 1=2 is fallacious.

10. July 1, 2015 at 11:52 am

Mistake here: why u said when 2b = b implies 2 = 1. Wrong man, if 2b = b then b = 0. U assumed that a = b then a = b = 0. The End

11. July 27, 2015 at 7:40 am

The problem stems from Step 4.

a+b=b

From here, you seemingly substitute a for b, because you go to the start of the equation and assume that the original statement is true – a=b

so it becomes
b+b=b.
or
2b=b

However, that is incorrect due to the fact that the original point hasn’t been proven yet and thus can not be used in the equation.

If i told you 2x=3y*4 and asked you to solve – you couldn’t just go:
2(3y*4)=3y*4
from the start.

So at step
a+b=b
you have to equalize the equation… subtract both sides by b.

a+b-b=b-b
a=0

From there, you can plug that value into the equation to see if the proof holds up… and it does.

12. May 15, 2016 at 9:17 am

How can you say 2b=b..then b=a..2b=a but your rule was a=b..that was wrong..next mistake is,when a=0,b also equal to 0..then 2b=b(your incorrect answer)2*0=0=0=0 is the answer..2nd row also wrong when we get a=b..b equal to a and a equal to b.then a^2 also equal to b^2..your system is wrong..algebra is right bro..

13. June 3, 2016 at 6:19 pm

a^2 = +/- a*b

14. July 14, 2016 at 2:47 pm

I need help…proof x=y

15. October 7, 2016 at 2:08 pm

you problem lies in

(a+b)(a-b) = b(a-b)

in line 3 you said ab-b^2 you cant take a factor of b out since its b^2 you have to square root b^2 because taking a factor of b out is assuming root b^2 is positive. but it can be negative too

(-b*-b = b^2 -b*-b != -b^2)

16. October 13, 2016 at 5:36 pm

wrong. to get from the fourth line to the fifth line, you have to divide both sides by (a-b), right? since a=b, a-b=0, and you cant divide by 0

17. November 7, 2016 at 3:30 pm

If a=b, then a-b is 0, so both sides are 0

18. November 15, 2016 at 1:29 pm

This is awesome

19. November 18, 2016 at 4:07 am

The flaw is from line 4 to line 5. The step you do, is that you dividi by (a-b). But a=b and therefor (a-b)=0. In other words, you have divider by zero, and you can’t do that. Sorry, but algebra is indestructable π

20. December 12, 2016 at 1:45 am

a=b then a-b=0 but dividing both side of equation by zero make equation false and cause error

21. January 9, 2017 at 11:56 am

Simple. A-b will be 0 and you are dividing by it in step four

22. March 19, 2017 at 3:48 pm

no you are wronngggggggggg yes frank is correct

23. July 27, 2017 at 2:14 pm

you cant divide by 0. eg 1 x 0 = y x 0