# Refute that 2+2=5x=y Let's say that x is equal to y.X²=xy multiply both sides by x.X² - Y² = XY - Y² substract Y² from both sides(x-y)(x+y)=y(x-y) factorize both sides(x+y)=y simplify...

Refute that 2+2=5

x=y Let's say that x is equal to y.
X²=xy multiply both sides by x.
X² - Y² = XY - Y² substract Y² from both sides
(x-y)(x+y)=y(x-y) factorize both sides
(x+y)=y simplify (x-y)
x+x=x if x=y you say write x instead of y
2x=x simplifying x variables
2=1
3+2=1+3 adding 3 to both sides
5=4
5=2+2

litteacher8 | High School Teacher | (Level 3) Distinguished Educator

Posted on

This is strange. Why not look at it as simply as a five year old. Draw 2 dots and then 2 more dots. Count the dots. One, two, three, four. There are four dots, not five dots. The above calculations are perfect examples of why we should not trust statistics! Numbers can be manipulated.

nathanshields | High School Teacher | (Level 1) Associate Educator

Posted on

Ugh - here's the complete version - sorry!

• Step 1: -1/1 = 1/-1
• Step 2: Taking the square root of both sides: sqrt(-1/1)=sqrt(1/-1)
• Step 3: Simplifying: sqrt(-1)/sqrt(1)=sqrt(1)/sqrt(-1)
• Step 4: In other words, i/1 = 1/i.
• Step 5: Therefore, i / 2 = 1 / (2i),
• Step 6: i/2 + 3/(2i) = 1/(2i) + 3/(2i),
• Step 7: i (i/2 + 3/(2i) ) = i ( 1/(2i) + 3/(2i) ),
• Step 8: (i^2)/2+(3i)/2i=1/(2i)+(3i)/(2i)
• Step 9: (-1)/2 + 3/2 = 1/2 + 3/2,
• Step 10: and this shows that 1=2.

nathanshields | High School Teacher | (Level 1) Associate Educator

Posted on

That's an old one - I don't want to give away the secret!  Here'a another good "proof" that 2 = 1, but requires a little knowledge of imaginary numbers:

• Step 1: -1/1 = 1/-1
• Step 2: Taking the square root of both sides:
• Step 3: Simplifying:
• Step 4: In other words, i/1 = 1/i.
• Step 5: Therefore, i / 2 = 1 / (2i),
• Step 6: i/2 + 3/(2i) = 1/(2i) + 3/(2i),
• Step 7: i (i/2 + 3/(2i) ) = i ( 1/(2i) + 3/(2i) ),
• Step 8: ,
• Step 9: (-1)/2 + 3/2 = 1/2 + 3/2,
• Step 10: and this shows that 1=2.

See if you can figure out in which step the fallacy lies.

accessteacher | High School Teacher | (Level 3) Distinguished Educator

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I remember a mathematician friend of mine telling me that actually 2+2 could equal five and then she embarked upon a whole complicated reason to explain why this was so, but it was a more philosophical and scientific debate than simply using equations as you have done above. In addition, as #2 indicates, there appear to be some erroneous equations in what you have done above.

wannam | High School Teacher | (Level 3) Educator

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This seems rather random to me.  Why are you multiplying both sides by x and then both sides by y squared?  If x=y then x squared would equal xy.  If x=y then x squared minus y squared would give you zero.  Yes, your third equation is technically correct, but I'm not sure why you would multiply both sides by y squared.  If x=y then we cannot say that x+y=y nor does x+x=x.  There are definite faults here.

najm1947 | Elementary School Teacher | (Level 1) Valedictorian

Posted on

Refute 2+2=5

The post 1 by  utkdmrz stars as under:

x=y Let's say that x is equal to y.
X²=xy multiply both sides by x.
X² - Y² = XY - Y² substract Y² from both sides
(x-y)(x+y)=y(x-y) factorize both sides

At step 3:

X² - Y² = XY - Y² substract Y² from both sides

and both the sides become ZERO.

This the starting point after which the whole arguments get messed up.

you have zeros on both sides, factorise in step 4 and then divide by x-y which is zero.

A division by zero is not permissible because its value is indeterminate, and if this is acceptible then the whole argument can be started as under:

Zero = Zero

Zero*(2+2) = Zero*5, divide both sides by Zero and we get:

2+2=5, I have proved it but it is absurd.

2+2=5

wanderista | Student, Grade 11 | (Level 2) Valedictorian

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I like post 8's response - never trust statistics, only use them as a guide and make sure you corroborate the information.

crread7 | High School Teacher | (Level 1) eNoter

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(x-y)/(x-y) is undefined it is not equal to 1. Which is the assumption that you made.

ragarm | (Level 1) eNoter

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It's simple. When you first simply, you divide by zero. You cannot divide by zero, not in any form. There are an infinite number of falacies that can be "proven" by this means.