Proving that 1+1=1 through Algebra?

Question

My maths professor said to our class that he will only consider anyone of us a genious if we can prove that 1+1=1 through algebra. I have tried and tried and tried, but i cant seem to do it. I have an idea whihc i will post as an answer, but im not sure ifs its completly right.

Answer 1

follow the algebra to prove that 2 = 1
a = x
a + a = a + x [add a to both sides]
2a = a + x [simplify]
2a -2x = a + x - 2x [subtract 2x]
2(a-x) = a -x [simplify both sides]
2 = 1 [divide both sides by a-x]

So there you have it, 2=1...

Everything in this equation is correct, apart from the very last step, since a and x are the same, you have actually divided by 0, and when you start doing that you get into the realms of infinity.

The fact of the matter is that 1+1 =2 and there is no way of making 1 + 1=1.

Answer 2

He is testing you out. Mathematics is the one science that can never be wrong. 1 +1 ALWAYS = 2 it can't equal anything else. What he's really after is to see you prove that using algebra. Even a genius couldn't prove something that isn't true. He may hoodwink you but, ultimately you'll always get the same answer. So, let's see if we can put something together for him.

Assume that the answer is an unknown quantity : x
Then if 1+ 1 = x then x MUST = 2
However if we bring x across and substitute it with 1 then we get
1 - x = -1 (So far x + 2 still)
Move the other 1 across and we get
-x = -1-1 so, suddenly -x + -2
Thus we have 2 answers. But, again, it's only playing around with figures.

All this proves that 1 + 1 = 2 and nothing else. Tell him that you are indeed a genius because you've proved that 1 + 1 does NOT = 1 and see what he says.

PS: Slider is wrong by assuming X + X = X. That's like assuming 1 + 1 = 1 which is the impossible object of the exercise in the first place.

Answer 3

This is very advanced mathematics, requiring understanding of group theory. 1 + 1 as we know it does equate to 1, but if we were to change the topography of the dimension and work within a characteristic two field, then 1 + 1 = 1

Answer 4

Meh I got showed this but forgot.

It involves a=1 and b=1 starting with a=b and at some point you divide by (a-b) which is 0 where it all goes wrong. By the way I have noticed obvious flaws in most of the above.

Edit: Actually sklaydonuk or whatever his name is has done it right :)

Answer 5

proving that 1 + 1 = 1 is a hard theory to prove.
I once said to my dad that 2 + 2 = 4, to which he replied 'no it doesnt it equals 2!' Of course this confused me and he explained. Just because both amounts are 1, it does not mean that their values are the same. The easiest way for me to explain this is to take the two '1's and to put them into a simple equation. 1x + 1b = 1. Confused? Okay we'll lable them. 1 bag of apples + 1 bag of oranges = 1. Yes it would equal 2 'bags' but thats not what we're after. It would equal '1' bag of apples and '1' bag of oranges. The quantities are the same but you can not place them together, therefore the answer is still one. Still lost?

Answer 6

Two simple ways to prove: in an algebraic system where + means multiplication, and also in a system where 1 means zero this is true by definition. This is first year of university stuff called group theory. I am telling you this as a Master of Mechanics and Applied Mathematics

Answer 7

Whoa!

"Mathematics is the one science that can never be wrong."

I wouldn't word it quite like that. Math is 'correct' based on many axioms, things we expect or accept to be true. If they are proven wrong then pervious mathematics which were once correct, are wrong. Remember that a proof doesn't always mean something is being proven *correct*. It is very possible and acceptable to prove something *incorrect*.

Proof's are an advanced concept. Here is a link to the proof of 1+1=2 from Whitehead & Russell's "Principia Mathematica".

http://humor.beecy.net/misc/principia/

I checked out a copy of "Principia Mathematica" my first quarter in college and cried myself to sleep every night trying to understand the first page.

Have fun. ;)

Answer 8

x+x = x have an answer and this answer is 0 so fi you divide this to x you will have 1+1= 1.
or
1 atom of hydrogen +1 atom of hydrogen = 1 molecule of hydrogen , this is 1+1=1 but the units of these 1s in this equivelance is diffrent.

Answer 9

I would be interested to see how 1+1=1 as well.

Use the equation X + X = X

thus

2X = X

subtract X from both sides

X = 0

and 0 is not 1

Answer 10

x,y,z = 0

x+1+y+1=z+1
x+y-z= -1

-x-y+z=1
0+0+0 doesn't equel 1

but 1-1-1= -1

that's the answer I guess