# 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 y2x=x simplifying x variables2=13+2=1+3 adding 3 to both sides5=45=2+2 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.
Approved by eNotes Editorial Team 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.
Approved by eNotes Editorial Team 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.

Approved by eNotes Editorial Team 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.

Approved by eNotes Editorial Team 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.

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