Math Riddle

[CK9]

I'm sure i've shown how to do this here before, so if you've seen the answer from me, please leave it for others to figgure out.


I can prove inequalities to be equal, that is to say, things that shouldn't add up to a certain number do.  Can you prove how:

2 + 2 = 3 ?

and

2 + 1 = 1 ?

[jcj94]

Powers of two?  2^0 + 2^1 = 1 + 2= 3

For the second.. I don't know :/

[Hidiot]

We define a system with the domain of all integers and a new operation (named # for the purpose of this proof), the function being: a # b = 2 - a + b.

plug in 2 and 1, and you get 2 # 1 = 2 - 2 + 1 = 1. By abuse of notation, we can rename # as + in our new system, so 2 + 1 = 1.

The whole point of our new system and operation is for 2 to be the neutral element in regard to the operation.

Edit: I took a closer look at this and realized that 2 is not a neutral element for this operation. This operation just happens to work.

[Hooman]

Hmm, I rather enjoy that answer Hidiot. Nice terminology.


Although, I should probably object to the "prove" part of the original question. Such "proofs" generally contain a hidden logical flaw that most people have trouble picking out. Like how squaring and square roots aren't perfect inverse operations.

As an example, sqrt((-1)^2) = 1  (not -1, as it would be if they were inverse operations).

You can probably use that fact in a creative way to make something appear to be like a proof. I can't bring myself to do it though.
 

[jcj94]

I honestly thought I was on to something...
Welp, yay for new math concepts.

[CK9]

no one has done it the way I'm thinking so far

Though, that is a very well thought out answer Hidiot

I'll give you all a hint:

in context of it's normal everyday use, this makes perfect sense.  Out of context, as it is presented here, it will make no sense at all.

[Freeza-CII]

first I need to harness the power of anti gravity particles. Then i need to use them on a black hole. then i need to fly my long skinny ship into the black hole. hopefully emerge on the other side where every thing is different and i die a horrible death maybe. but then just then in the nano seconds before my death 2+2 would equal 3 with out any sort of trick or mathmatical know how.

[evecolonycamander]

I see how it is possible if you merely replace the numbers with a variable such as X. so:
2 + 2 = 3 ?
Is
X + X = 3 ?

AND

2 + 1 = 1 ?
Is
X + Y = 1 ?

X= 1.5
Y= -0.5

[CK9]

no...that is just an invalid argument...that's like saying "I'm replacing the elephant with a quarter, so yea, the elephant fits in my pocket"

[jcj94]

"I'm replacing the elephant with a quarter, so yea, the elephant fits in my pocket"

Thats just the way ECC works.

I brought this problem up in first one day and yeah, the way Hidiot showed us was what we used.
 

[CK9]

One more hint before I end up giving the answers:

while it is a math problem, it isn't a direct math problem.  Think about the applications of math in other areas.

[Hidiot]

Thinking graphically (as in, the shapes of the numbers):
Take a 2 and invert it by its base. Now overlap the base of the inverted 2 with the base of the standard 2, and you get a shape that looks almost like a 3. You'd need to remove the line to get an actual 3.

Also, 2 H + 1 O =1 H2O.

[CK9]

Hidiot got the second one semi-correct, lol (my fault though, I wasn't thinking empiricly when I was typing, heh)

[jcj94]

I give, I don't know about you guys though.. PM me the answer?  I promise I wont post it

[CK9]

I'll just post it.  It has to do with groups of different objects.

For example:

An apple and an orange is a group of two DIFFERENT fruits.  An apple and a pear is another group of two DIFFERENT fruits.  If we add these together, we end up with a group of three DIFFERENT fruits.  Thus, in this example with its context, 2 + 2 = 3

[jcj94]

Oh, darn.  That.. wow.  I was over thinking that A LOT...

[Hooman]

Sounds like Hidiot was on to something when he said redefine the "+" symbol to be a different operator.

You're talking about cardinality and set union.
A + B
|A U B|

Mind you, trying to fit that into an equality still doesn't quite work without some serious abuse of notation. You would need to use the same symbol to represent both a set, and the cardinality of that set.
 

[CK9]

no, I'm just talking about adding things together

In all seriousness, though, it's just ment to make people think.  Rather than accept that something is true, find out why it is true.