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Math Geek proof that FOUR EQUALS THREE

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by Lawrence J. J. Leonard

This is how to prove 4 = 3.  If you are a Math Geek, kinda like me, then you will enjoy this trick to fool your friends. There is always a catch, though.

Let’s assume this expression is true: a + b = c
This can also be re-written as:
4a – 3a + 4b – 3b = 4c – 3c

So far, so good.  All true.

Now Reorganize:
[-4c]  4a – 3a + 4b – 3b = 4c – 3c [-4c]
4a – 3a + 4b – 3b – 4c = -3c      .Okay.

[+3a+3b] 4a – 3a + 4b – 3b – 4c = -3c [+3a+3b]
4a + 4b – 4c = 3a + 3b -3c        .Okay.

Remove common factors:
[4]   4a + 4b – 4c =  3a + 3b – 3c   [3]
This is the result:
4 (a+b-c) = 3 (a+b-c)

Extract the Common Terms on both sides.
They cancel each other out.
4 = 3

This is known as a “Howler” or blunder because it is based on a fallacy of multiplication — The coefficients, in this case 4 and 3, are dependent on what is in the brackets.

If a + b = c, then when you ‘remove common factors,’
what is in the brackets will equal zero — because of the “-c” (negative c).

Remember the equation you are left with is, in actuality, this:  4(0) = 3(0)
This is true only if you multiply the coefficients.
This is true without the coefficients.
This is **not true** if you ignore the PEMDAS rule, and get 4=3. (Ooooo!)

How Do I remember the PEMDAS rule?
P     – Parentheses first
E     – Exponents (i.e. Powers and Square Roots, etc.)
MD  – Multiplication and Division (left-to-right)
AS  – Addition and Subtraction (left-to-right)

Copyright © 1960-2015 Lawrence J. J. Leonard  All rights reserved


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