Question

Mathematical challenge.

Today i am going to present the theorem of the identity of a number and its double.

It says that any real number is equal to its double...
1 = 2
10 = 20

How?

Right now, in an answer, i am going to show the process for do it. Obviously, this is invented by my math teacher.

Your challenge will be to find the mistake in the process i am going to put now as an answer Mathematical challenge.

Today i am going to present the theorem of the identity of a number and its double.

It says that any real number is equal to its double...
1 = 2
10 = 20

How?

Right now, in an answer, i am going to show the process for do it. Obviously, this is invented by my math teacher.

Your challenge will be to find the mistake in the process i am going to put now as an answer @Mathematics

Answer 1

these are fun :)

Answer 2

I. We put two variables of the same value.

\[A = 1\]
\[B = 1\]
Then, \[A = B\]

II. We multiply both sides by A (remember that if you do something to one side, you do the same to the other side).
\[A ^{2} = AB\]

III. We subtract \[B ^{2}\] to each side.
\[A ^{2}-B ^{2} = AB - B ^{2}\]

IV. We factorizze
\[(a+b)(a-b) = b(a-b)\]

V. We divide each side by a-b
\[(a+b)(a-b)\div a-b = b(a-b) \div a - b\]

VI. Answer

A + B = B
2 = 1

Find the mistake!!

Answer 3

im sure people will find it, this ones very common. :)

Answer 4

can't divide by a-b because that's 0

Answer 5

yep...that was fast xD

Answer 6

heres a good calculus one.

Answer 7

what went wrong o.O *gasp*

Answer 8

\[\sum_{1}^{x} 1 \neq x\]

???

Answer 9

why doesnt it?

I add 3 ones I get 3. I add 5 ones I get 5. I add x 100 ones I get 100.

So why wouldnt it be true that when I add x ones I get x?

(you are on the right path btw, theres a more concrete way of saying what you mean though, good job!)

Answer 10

V. is the mistake you cannot divide by a-b because a-b is zero

Answer 11

oops, "if i add 100 ones I get 100", typo on that "x" >.<

Answer 12

Yes UnkleRhaukus...now we are talking of another challenge

Answer 13

I don't have a clue! Hahaha, help me out!

Answer 14

in order to take the derivative of a function, the function must be continuous over the domain of integration. The function:\[\underbrace{x+x+\cdots+x}_{x \mbox{\times}}=x^2\] does hold for integers....but what about fractions? or irrational numbers? does it makes sense to add "4/5" 4/5 times? or square roots of 2 square root of 2 times? nope!

So this function is only defined on positive integers. Its not continuous, so you cant take the derivative.

Answer 15

...i dont know why i said integration... i meant over the real numbers.

Answer 16

im tired >.< my bad.

Answer 17

Those dumb rules! >.< I'm gonna show everyone :)