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Forums - General Discussion - Can you scientifically prove to me that 2+2= 4?

Grey Acumen on 13 October 2008
theprof00 said:
dtewi said:

I'll mathematically prove it to you.

  • This is easily demonstrated
  • Add to both sides
  • This can be factored
  • Take the square root of both sides
  • Now add to both sides
 

Using properties of equality, we can makes this 2+2=5. Wait...

Nice parlor trick, but, you fail for injecting non-equal numbers into an equation in step one, i guess this works well among your fellow 7th graders though :P

http://us.metamath.org/mpegif/2p2e4.html

um, 4 - 6 = -2

and 1 - 3 = -2

so how are these inequal? tarheel actually got to the crux of this issue, which is that square roots have both positive and negative answers. This was further disguised by leaving each root as a positive integer minus a fraction of a value greater than one.



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Soleron on 13 October 2008

No. You can't.

All mathematics is based on fundamental, self-evident properties called "axioms". All theorems must be proven using these axioms or other theorems, but the axioms themselves can never be proved.

Look at Godel's theorems if you're interested in some consequences of that.



masterb8tr on 13 October 2008

^indeed

Also 5+5=10 but 5+5 also equals 5. Funny huh



NJ5 on 13 October 2008
Soleron said:
No. You can't.

All mathematics is based on fundamental, self-evident properties called "axioms". All theorems must be proven using these axioms or other theorems, but the axioms themselves can never be proved.

Look at Godel's theorems if you're interested in some consequences of that.


But "2 + 2 = 4" is not an axiom (at least not in most mathematical systems), it's a theorem. Therefore, it can be proven.

 



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mesoteto on 13 October 2008

i just did, now using science prove that i didnt



 

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Tispower1 on 13 October 2008
NJ5 said:

The starting point is the definition of the numbers 2, 3 and 4, and the associative property of addition:

(a + b) + c = a + (b + c)

Using the inductive definition of natural numbers, the definitions of 2, 3 and 4 are:

2 = 1 + 1
3 = 2 + 1
4 = 3 + 1

You can then replace the 3 by 2 + 1

4 = (2 + 1) + 1

Using the associative property of addition, the equation becomes:

4 = 2 + (1 + 1)

But the definition of 2 is "1+1", so:

4 = 2 + 2

That's the best I can do right now, seems like a reasonable proof relying only on one axiom. Obviously we have to rely on something to start up the proof, since nothing can be proved from nothing.

 

 

Makes sense.



Soleron on 13 October 2008
NJ5 said:
Soleron said:
No. You can't.

All mathematics is based on fundamental, self-evident properties called "axioms". All theorems must be proven using these axioms or other theorems, but the axioms themselves can never be proved.

Look at Godel's theorems if you're interested in some consequences of that.


But "2 + 2 = 4" is not an axiom (at least not in most mathematical systems), it's a theorem. Therefore, it can be proven.

 

 

...yes, you're right. Nice proof. Proving  a+(b+c) = (a+b)+c is impossible though.



NJ5 on 13 October 2008
Soleron said:
NJ5 said:
Soleron said:
No. You can't.

All mathematics is based on fundamental, self-evident properties called "axioms". All theorems must be proven using these axioms or other theorems, but the axioms themselves can never be proved.

Look at Godel's theorems if you're interested in some consequences of that.


But "2 + 2 = 4" is not an axiom (at least not in most mathematical systems), it's a theorem. Therefore, it can be proven.

 

 

...yes, you're right. Nice proof. Proving  a+(b+c) = (a+b)+c is impossible though.

Not necessarily impossible, depending on which axioms your mathematical system has.

I think I get your point though... Axioms are always needed in a mathematical system. However, every science relies on something it does not prove. Another way of putting it is as I said above "nothing can be proven from nothing".

 



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dtewi on 13 October 2008

That was just a simple trick I got off a random website.

2+2 is most certainly not equal to 5.

Do you want me to show you two others so you can prove it wrong?



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mesoteto on 13 October 2008

best i cna do is 1+1=3

one male plus one female= one male/one female/ and one child