Proof that 1=2

Off-topic
1

Hey guys, check out this proof that shows, using simple algebra, that 1 actually equals 2.

Assume: a = b
1.multiply both sides by a
a^2 = a*b

  1. subtract b^2 from both sides
    a^2-b^2 = a*b-b^2

  2. apply the distributive law to both sides
    (a+b)(a-b) = b(a-b)

  3. divide both sides by (a-b)
    (a+b) = b

  4. substitute all a’s for b’s (remember, if a = b you can do this)/
    a+a = a

  5. regroup the two a’s in the left side, and rename it 2a
    2a = a

  6. divide both sides by a
    2 = 1

My friend showed me this last year. I just remembered it and decided to share. Can anyone find the mistake? Try to find it yourself before seeking help from the responses or any help at all from that matter.

2

The mistake? He used algebra, that was simple. You can’t do better than that?

3

the mistake is you divide by 0.

4

bravo

5

thank you.:smiley: i love math. my calculus teacher showed this one day in class.

6

sorry i killed your thread so early too.:smiley:

7

yes without even reading it i can guess it’s a div zero problem, these things always are.

8

I have an interesting theory that might keep this thread open, but not relating to its name.

Is it possible to find the square route of a negative number, my mathematics teacher keeps telling us it’s impossible and the answer doesn’t exist, but something in the back of my mind keeps pushing it back into my thoughts. I need an answer!

9

umm…errr…um… Actually i never thought of that b4. I wonder too if it somewhat possible. :thinking:

10

Yes you can, it’s called a imaginary number.

The root of -1 is called i. This can be multiplied by other number to create other negative roots i.e. the root of -9 is 3i.

11

And technically your teacher wasn’t lying i stands for imaginary, and imaginary number do no exist, instead they get substituted by the letter i for Algebraic purposes. Now you can go into class and show eerybody up!

12

In algebra, however, you can substitute i for a route of a negative number and then eventually when solving a equation or something it can “turn” back into a real number (I don’t know if that made sense). What I am trying to say is that imaginary numbers aren’t completely useless, though it has been awhile (about 2 years) since I’ve covered them in depth.

13

This works fine! Just look at the quatum physics side of things.

14

I must confess, I’m afraid I fail to understand what you are trying to say.

15

She also apparently said it was impossible. It is not. Imaginary numbers exist, they just don’t fall in to the sub-group ‘real numbers’. i is a number in the same way pi is a number, but it cannot be represented on a number line the way pi can, it requires a 2 dimensional Argand diagram.

16

Eh, you can see pi in action in front of your eyes (for those who didn’t know, pi is simply the amount of times you multiply the diameter by to get the circumference). To the extent of my knowledge, imaginary numbers cannot be seen in any way really.

Pi is an irrational number, not an imaginary number. Irrational and imaginary numbers are two completely different things.

Edit: but really, the keyword here is imaginary NUMBER, these are all numbers.

17

wow i am slightly confused now. I got the first thing, but 2 dimensional Argand diagrams? I was told that you can’t get the square route of a minus number so dont try, and I havent tried. Teachers aren’t that dumb (except from choosing to go back to school :astonished: ), when it gets to teaching they usually know what theyre on about so just go with what they say.

18

Are you sure you’re teacher didn’t say, “don’t try this since you don’t know how to do this yet”? or something a long the lines of that.

Or even more likely “There is no REAL solution to this”. That would be true, there is only an imaginary solution. Perhaps that is what she meant. If she said it was impossible, and there is no way to deal with square routes of negative numbers, I would take away her teaching license, or if I was nice I would just make her teach Kindergarten.

19

Put yourself in your teacher’s shoes. She/He probably very well knows that you can find the square root of a negative using i. She also knows that normal square roots are a hard concept to teach and if she starts throwing out imaginary numbers NOW, a few years before you normally learn them, the students will just get more confused.

Sometimes it’s easier to say you can’t do it than say “well, you can, but that’s super complicated and you’ll learn it later.” A lot of kids won’t accept that answer and it will just screw the whole class up.

I would just not mention them at all, but if someone asked tell them to come up later and that you’ll explain it. That way the whole class doesn’t get gunked up. Too much information at once is a recipe for failure when teaching math.

20

All true, all irrelevant.

whether you see a number infront of your eyes or not makes no difference to whether it exists or not. Everytime i analyse an electronic circuit i see imaginary numers everywhere.

I used pi as an example of a common algebraic representation of a number. I could have used x where x=2 but it would have required more explanation. The fact that pi is irrational has precisely nothig to do with my argument, it was simply a number that you can spot on a number line, somewhere between 3 and 4.