1x1=2

[Freodin]

I still love how that's a distinction that exists: real maths and real maths.

Not "maths"... "math equations".

Problem is that math uses an expanded set of typography. Standardized symbols to simplify rather complex structures.
This is not possible to display with the "common" set of letters... or possible to "correctly" display by the common text structuring.

 

[Warden_of_the_Storm]

Not "maths"... "math equations".

Problem is that math uses an expanded set of typography. Standardized symbols to simplify rather complex structures.
This is not possible to display with the "common" set of letters... or possible to "correctly" display by the common text structuring.

First of, I'm British, so I'm going to spell it as maths. Queen's English, bru.
And secondly, you're talking to guy who had to take his maths exam twice, so almost all of what you say is going to go over my head.

 

[crjmurray]

I'm loving this...

 

[Freodin]

This forum doesn't even implement BBCode sub- and superscript. Makes it really difficult to write out more complex mathematical equations.

Let's try for something really headache inducing:

ln ( lim [v->∞] (1+(1/v))^v) +(sin(q)^2+cos(q)^2) = Σ [0<=n<=∞] ( cosh(p) * sqr(1-tanh(p)^2) / 2^n)

 

[crjmurray]

This forum doesn't even implement BBCode sub- and superscript. Makes it really difficult to write out more complex mathematical equations.

Let's try for something really headache inducing:

ln ( lim [v->∞] (1+(1/v))^v) +(sin(q)^2+cos(q)^2) = Σ [0<=n<=∞] ( cosh(p) * sqr(1-tanh(p)^2) / 2^n)

Oh your God, somebody call 911 I think freodin had a stroke while typing.

 

[leftrightleftrightleft]

This forum doesn't even implement BBCode sub- and superscript. Makes it really difficult to write out more complex mathematical equations.

Let's try for something really headache inducing:

ln ( lim [v->∞] (1+(1/v))^v) +(sin(q)^2+cos(q)^2) = Σ [0<=n<=∞] ( cosh(p) * sqr(1-tanh(p)^2) / 2^n)

 

[Freodin]

Almost. How did you do that?

 

[leftrightleftrightleft]

Once I found out that the square root of a negative number is an imaginary number, I figured all math was suspect.

Just another type of number.

Math is just symbols after all. Imaginary (or complex) numbers are just a useful way of describing circles and waves.

 

[leftrightleftrightleft]

Almost.

Did I miss a bracket?

How did you do that?

I cheated with this online latex editor. Relatively easy to copy paste figure hyperlink into forum window.


If you're desperate...

 

[Freodin]

Did I miss a bracket?

The expressions "[v->∞]" and "[0<=n<=∞]" should have been put in subscript. That's all.
(Nah, that's not all! In the last part, the "/2^n" needs to be outside of the square root) Always check thrice! )

I cheated with this online latex editor. Relatively easy to copy paste figure hyperlink into forum window.


If you're desperate...

If you are addicted to math... well, it's better than meth, isn't it?

 

[Freodin]

BTW... this horribly complicated expression comes down simply to "1+1=2". Math nerds' joke.

 

[Chriliman]

Huh?

How do you ever get to the 1+1=1 part?

You are correct a+a=2. b+b also equals 2. (Assuming a and b are 1). But so would a+b equal 2.

Saying:

If a=1, then 1≠b

is logical, whereas saying:

If a=1, then 1=b

is illogical or at least requires more explanation than the first.

That is the logic I'm trying to convey.

 

[Tree of Life]

1 occurring 1 times amounts to 1. That's another way of saying 1x1=1.

If this dude believes 1x1=2 then he also must believe that (1x1)/2=2/2, which could be simplified to .5=1

And he must also believe that (1x1)/1=2/1 which would be simplified to 1=2.

So if .5=1 and 1=2 then 1x1 does indeed equal 2. Maybe he is onto something...

But if 1=2 then 1x1=2 could be amended to say 2x2=2 or 2x2=1

Also if .5=1 and 1=2 as his mathematics would say then .5=2 and 1x1=2 would be identical to 2x.5=1. Since this last equation is actually correct I would conclude that this gentlemen is right.

 

[ViaCrucis]

Saying:

If a=1, then 1≠b

is logical, whereas saying:

If a=1, then 1=b

is illogical or at least requires more explanation than the first.

That is the logic I'm trying to convey.

If a = 1 and b = 1, then a = b because 1 = 1. That is completely and intrinsically logical.

-CryptoLutheran

 

[Freodin]

Saying:

If a=1, then 1≠b

is logical, whereas saying:

If a=1, then 1=b

is illogical or at least requires more explanation than the first.

That is the logic I'm trying to convey.

No, no, no, please, Chriliman. Look back at what you wrote earlier.
"Always assume there is someone who knows more than you do and that you can learn something from them."

"a" and "b" are just two seperate variables. Two seperate expressions that can be filled with values, or assigned to seperate attributes. They do not depend on each other.

So simply saying "if a = 1, then b ≠ 1" is not "logical". Just as simply saying "if a = 1, then b = 1" is not "logical". There is not yet any relation established between a and b.
Such a relation needs to be established, either by definition or by calculation.

For example:

Let a be the number of dollar bills in your wallet. Let b be the price of bread in dollars. c will be the number of loafs of bread you can buy. c=a/b

Now to fill it with values. Assume you have ten dollars, and the price of bread is two dollars per loaf.

a=10, b=2
c=a/b
c=10/2
c=5
​

You can buy five loafs of bread.

Or you have one dollar, and the price of bread is one dollar per loaf.

a=1, b=1
c=a/b
c=1/1
c=1
​

Just one bread now. See, different variables... same value. In this case, even three variables with the same value! Got it?

Another example:
The famous "Pythagorean theorem": in any triangle with one right angle (90°), the square of the side opposite the right angle (the hypotenuse, called "c") is equal to the sum of the squares of the other two sides (the catheti, called "a" and "b").
You certainly have heard it or read it somewhere... "a squared plus b squared is c squared"

Example: Right angled triangle, the cathetus a = 3, the cathetus b = 4. What is the length of the hypotenuse?

c^2 = a^2 + b^2
c = sqr (a^2 + b^2)
In this case: c = sqr(3*3 + 4*4)
c = sqr(9+16)
c = sqr(25)
c = 5
​

Example: Right angled triangle, cathetus a = 1, hypothenuse c = sqr(2). What is the length of the other cathetus b?

Again: c^2 = a^2 + b^2
Thus: b^2 = c^2 - a^2
b = sqr(c^2 - a^2)
In this case: b = sqr( sqr(2)*sqr(2) - 1*1)
b = sqr(2 - 1)
b = sqr(1)
b = 1.... equal to what a is.
​

Different variables, denoting different attributes... same value.

It's not rocket science, or brain surgery. Just simple algebra.

 

[Freodin]

First of, I'm British, so I'm going to spell it as maths. Queen's English, bru.

So "a+b=c" is "a math"? Never heard that before!

I also couldn't find this definition in the Oxford Dictionary... though I did find "formula" and "equation". I guess it might be British English... but Queen's English? And "bru"? Come on, you are pulling my leg!

Eferivon nos sat ve Tshermans shpeak se best Queen's English!

[/Grammar Nazi]

 

[Warden_of_the_Storm]

So "a+b=c" is "a math"? Never heard that before!

I also couldn't find this definition in the Oxford Dictionary... though I did find "formula" and "equation". I guess it might be British English... but Queen's English? And "bru"? Come on, you are pulling my leg!

Eferivon nos sat ve Tshermans shpeak se best Queen's English!

[/Grammar Nazi]

I don't know how it works. My main area of interest in study was military history, not history of linguistics. Although I do know that, historical, the English language has never made the most sense.
And Queen's English is an actual term, although it's just another term for the style pronunciation in Southern England, aka Posh English.

And bru's South African. I liked Di Caprio's character in Blood Diamond.

 

[Quid est Veritas?]

I don't know how it works. My main area of interest in study was military history, not history of linguistics. Although I do know that, historical, the English language has never made the most sense.
And Queen's English is an actual term, although it's just another term for the style pronunciation in Southern England, aka Posh English.

And bru's South African. I liked Di Caprio's character in Blood Diamond.

Bru is derived from the Afrikaans Broer meaning Brother as English often makes the final R non-rhotic, like in Eyeore from Winnie-the-Pooh whose name is actually equivalent to heehaw for donkey sounds.

 

[Quid est Veritas?]

As to this conundrum, you are all wrong. Note: I am using Axiom in the Epistemological sense or 'Philosophy of Mathematics' sense and not the standard sense of Axiom in Mathematics.

Mathematics as a system is based on a few unprovable assumptions or axioms. Amongst these are 1 +1 =2; 1 x 1 = 1 etc. They are axioms as we all say "yes, that is right" without it ever being proven as such. They are self-evident we could say. We are taught proofs for Pythagoras's theorum for instance, but never for these most basic of statements. Most just accept it is correct.
Even making statements like "you have 1 and add 1 to make 2" remain axiomatic. Why not get 3 or 715.21? It has never been proven, only accepted as logical it is 2.

So if someone alters the answer to a base axiom of Mathematics, he creates a fully acceptable variant Mathematics which is as valid as our normal one. The axioms aren't proven as such and even if we disagree with his axiom, to HIM it is as plain as the nose on your face and remains axiomatically valid. Maybe the rest of us are wrong after all.

So while not correct in standard Mathematics, there is nothing inherently wrong about 1 x 1 = 2.
In "True Mathematics" this might be the case, for there is no reason to assume that just because the vast majority of humanity agrees that 1 x 1= 1 is obviously true, that it MUST be.

 

[Freodin]

As to this conundrum, you are all wrong. Note: I am using Axiom in the Epistemological sense or 'Philosophy of Mathematics' sense and not the standard sense of Axiom in Mathematics.

Mathematics as a system is based on a few unprovable assumptions or axioms. Amongst these are 1 +1 =2; 1 x 1 = 1 etc. They are axioms as we all say "yes, that is right" without it ever being proven as such. They are self-evident we could say. We are taught proofs for Pythagoras's theorum for instance, but never for these most basic of statements. Most just accept it is correct.
Even making statements like "you have 1 and add 1 to make 2" remain axiomatic. Why not get 3 or 715.21? It has never been proven, only accepted as logical it is 2.

So if someone alters the answer to a base axiom of Mathematics, he creates a fully acceptable variant Mathematics which is as valid as our normal one. The axioms aren't proven as such and even if we disagree with his axiom, to HIM it is as plain as the nose on your face and remains axiomatically valid. Maybe the rest of us are wrong after all.

So while not correct in standard Mathematics, there is nothing inherently wrong about 1 x 1 = 2.
In "True Mathematics" this might be the case, for there is no reason to assume that just because the vast majority of humanity agrees that 1 x 1= 1 is obviously true, that it MUST be.

That is not quite correct.

You are correct though that all mathematical systems are based on unproven axioms, which are taken as "obvious truths". But you are not correct in identifying these axioms. Neither "1+1=2" nor "1x1=1" are axioms... they are definitions.

For example, there is a mathematical concept called "field" (I had to google that, in German it is called a "Körper"... a body ). A field is a bunch of elements (not even necessarily "numbers") and operations (usually called addition and multiplication, but not necessarily the "normal" kind) where certain rules apply. Like: "any operation done on an element of the field always results in an element of the field".

Another rule of a "field" is "there exists a "neutral" element for operations, where any operation done on one element with that neutral element results in the original element" Mathspeak: "x + n_add = x , x * n_mult =x"

The set of natural numbers form such a field. The neutral element for multiplikation is said to be "1". Thus 1 * 1 = 1.

"2" is just the definition for the element that follows "1" in the set of natural numbers.

But now there is an axiom: "for every element n in the set of natural numbers, there exist an element n+1" Unproven, unprovable... but obviously correct.

Mathematics is awesome.