Does anyone know the proof that states that 4=5?

Question

There is a site somewhere and i cant find it

Answer 1

If you look at Wikipedia under 'Invalid Proof' there's one that 4 equals 5.

Start with the identity:
-20 = -20

Express both sides in slightly different, yet equivalent ways:
16 - 36 = 25 - 45

Factor both sides:
4^2 - 4 x 9 = 5^2 - 5 x 9

Complete the square by adding 81/4 to both sides:
4^2 - 4 x 9 + 81/4 = 5^2 - 5 x 9 + 81/4

Factor both sides again:
( 4 - 9/2 )^2 = ( 5 - 9/2 )^2

Take the square root of both sides:
4 - 9/2 = 5 - 9/2

Cancel the common factor:
4 = 5

There is obviously a flaw in this logic and it is when you take the square root of both sides. At that point your really have (-1/2)² = (1/2)² but it is disquised. If you have x² = y², that doesn't mean x = y. It means x = +/-y.

Anyway, try it on your friends and maybe they won't catch the flaw.

Answer 2

-----Proof 1
Given
a = b ≠ 0
a² = ab
a² - b² = ab - b²
(a + b)(a - b) = b(a - b)
a + b = b
b + b = b
2b = b
Since b ≠ 0
2 = 1
1 = 2
1 + 3 = 2 + 3
4 = 5




-----Proof 2:
-20 = -20
16 - 36 = 25 - 45
16 - 2(36/2) = 25 - 2(45/2)
16 - 2(36/2) + 81/4 = 25 - 2(45/2) + 81/4
(4 - 9/2)² = (5 - 9/2)²
4 - 9/2 = 5 - 9/2
4 = 5




-----Proof 3
Property:
If
b^x = b^y, then
x = y

1^4 = 1^5
Therefore,
4 = 5




-----Proof 4
1 = 1
Multiply ∞ (infinity)
∞ = ∞

since you know that
4 · ∞ = ∞
and
5 · ∞ = ∞
Therefore,

4 · ∞ = 5 · ∞
Divide by ∞
4 = 5




-----Proof 5
1 = 1
Since you know that
4^0 = 1
5^0 = 1

Therefore
4^0 = 5^0
4 = 5




-----Proof 6
Given
1 = 1
Multiply by ∞
∞ = ∞
since
4^∞ = ∞
5^∞ = ∞
4^∞ = 5^∞
4 = 5




-----Proof 7
Given
1 = 1
Multiply by ∞
∞ = ∞
since
∞ + 4 = ∞
∞ + 5 = ∞
∞ + 4 = ∞ + 5
4 = 5




-----Proof 8
Given
1 = 1
Multiply ∞
∞ = ∞
since
∞^4 = ∞
∞^5 = ∞
∞^4 = ∞^5
4 = 5



-----Proof 9
given
0 = 0
SINCE
0^4 = 0
0^5 = 0

0^4 = 0^5

Since
b^x = b^y then x = y

4 = 5


QED
^_^

^_^
^_^

Answer 3

I will show the errors in all of kevin!'s previous "proofs."

1. He divided both sides by (a-b) when a = b, thus he divided by zero. Bad kevin!.

2. When he took the square root of both sides, he took the negative square root on the left side, because (4-9/2) is negative. This is not allowed.

3. This property does not apply to b = 1 nor b = 0 by definition.

4. Infinity is not a number. You cannot do arithmetic nor exponential operations on it to obtain results.

5. This really proves nothing... Any integer raised to the power of 0 is 1, making this proof invalid.

6, 7, 8. See 4.

9. See 3.

It's safe to bet any proof that concludes that 4=5 has broken some rule and is therefore invalid.

I win.

Answer 4

Here is 1+1=3

Start:
-8 = -8
4 - 12 = 16 - 24
4 - (6 + 6) = 16 - (12 + 12)
4 - (6 + 6) + 9 = 16 - (12 + 12) + 9
factor:
(2 - 3)² = (4 - 3)²
2 - 3 = 4 - 3
2 = 4
divide by 2
1 = 2
Add 1:
1 + 1 = 3

Answer 5

Just so you know, when you do find the site, read the proof very very carefully. If you are well educated in math you will be able to find the goof. I have seen these on many occasions, people don't catch them and that is why they are so surprised that 4=5 etc...when it really doesn't....the person that posted the proof above screwed up at the factoring part for instance...

Answer 6

There is an exercise, where you hide the fact that you are dividing by 0 to "prove" that 0 = 1. By extention, you can prove that 4 = 5.

Since it is based on bogus mathematics, it doesn't qualify as the proof of anything.

If you look around, you can find it in a previous answer. The same question gets asked and answered two or three times every day.

Answer 7

This is probably the easiest way:

x = 4 subtract 4 from each side
(x - 4) = 0 mulitply each side by (x - 5)
(x - 4)(x - 5) = 0 divide each side by (x - 4)
(x - 5) = 0 so
x = 5

The equation in the middle legitimately has two answers,
x = 4 and x = 5 (it is a parabola so this is ok). I lose
one solution when I incorrectly allow a division by
zero.

EDIT:
That post below mine is so wrong in so many ways.
You can't round 4.9999 (repeating) to 4 and
4.999 (repeating) is identically equal to 5 (not just close).

Answer 8

4^0 = 5^0

Answer 9

I have seen this proof before also. The lesson to be learned with this proof is that you are dividing by zero and when you do that, it introduces the incorrect solution of 4=5.

Answer 10

I don't think there is any way to prove 4=5...it's like saying 1+1=3...unless the proof is unconventional joke....like the TIME=MONEY proof :-P