1+1=?

[Sabejias]

That is a paradox. If something infinite reaches a finite point it is not infinite.

I don't get how you can think that 0.9r = 1
0.9r + 0.0r1 = 1

0.0r1=0. Duh!
.000000000000000000000000000000000000000000000000000000000...1!

I know of another way to prove that 0.9r=1.

Let x=0.9r
10x=9.9r
(.99999999999999999999...*10=9.99999999999999999999...)
10x-x=9.9r-0.9r
9x=9
x=1
0.9r=1

See?
No divide by 0s or any of that mathematical nonsense!

 

[Sabejias]

9 rounds up you poo-poo eaters!..im the only person to get that....jeez....so when repeating finally gets to google(the highest number). it rounds up

What about google+1? eh?
And then 2*google.

 

[superluminal]

No,

If x = 0.9r

then 10x = 9.0r

You can't just go adding shit to one side at will. This is stupid.

 

[shmoe]

No,

If x = 0.9r

then 10x = 9.0r

I think the 'r' was supposed to stand for repeating, 0.9r=0.99999...


One thing I wish though is that people wouldn't write crap like 0.0r1=0.00...001, like there's some kind of last decimal place after an infinite number of other digits. Sigh.

 

[superluminal]

Jeeze. Looked like a variable to me. Then again, I was expecting conventional notation. Silly of me.

 

[Crunchy Cat]

Holy shit batman, why is this thread still alive? 1+1=2 and 1x+1y<>2 if the x
& y quantities dont balance the left side of the equation. Somsone shoot
this thread please!

 

[superluminal]

Bang!

 

[Sabejias]

In math, why would you have to spend 300+ pages proving that 1+1=2. Isn't that the definition of 2?

I apologize for my usage of r. I noticed that other people were using it.

 

[Nasor]

In math, why would you have to spend 300+ pages proving that 1+1=2. Isn't that the definition of 2?

I suspect that most of the proof dealt with proving that 1+1 always equals the same thing.

 

[Sabejias]

I suspect that most of the proof dealt with proving that 1+1 always equals the same thing.

That seems pretty sad. I hated having to do all these proofs in high school.
BASIC INUITION!!!

Actually, reflexive property of equalitiy: 1+1=1+1
Definition of 2: 1+1=2
Transitive property of equality: 1+1=2

 

[Nasor]

Actually, reflexive property of equalitiy: 1+1=1+1
Definition of 2: 1+1=2
Transitive property of equality: 1+1=2

But again, you just assume that 1+1 must always equal the same thing. Maybe sometimes 1+1 equals one thing, and other times it equals another. Then you could only define "2" as "the result of 1+1" if you were willing to allow 2 to have more than one value.

Of course it seems intuitive that 1+1 could only ever result in one possible value, but in math that doesn't count for much. Intuition is often wrong.

 

[Sabejias]

But again, you just assume that 1+1 must always equal the same thing. Maybe sometimes 1+1 equals one thing, and other times it equals another. Then you could only define "2" as "the result of 1+1" if you were willing to allow 2 to have more than one value.

Of course it seems intuitive that 1+1 could only ever result in one possible value, but in math that doesn't count for much. Intuition is often wrong.

Reflexive property of equality. For any a, a=a. if a is defined as 1+1, then by reflexivity, 1+1 always equals 1+1.

 

[Nasor]

Reflexive property of equality. For any a, a=a. if a is defined as 1+1, then by reflexivity, 1+1 always equals 1+1.

Yes, but this doesn't prove that 1+1 can only ever have one possible value.

By the reflexive property of equality 4^0.5 = 4^0.5, but 4^0.5 could equal +2 or -2. How do we know that there aren’t more than one possible answer for 1+1, just as there are more than one possible value for 4^0.5? I could see it taking many pages of set theory to prove that.

 

[Sabejias]

Good point.

 

[Breaker]

1+1=whater the value of 1 may equal. In cryptology we use this inorder to encode things for example:"1"=5 and "2"=6 then 1+2=11
This has to be the only way other than change of base that 1+1 may equal something other than 2.

 

[Pete]

How many legs does a dog have if you call the tail a leg?
Four. Calling a tail a leg doesn't make it a leg.

- Abraham Lincoln

I don't necessary agree with Mr Lincoln, but I acknowledge his point.

 

[el-half]

One thing I wish though is that people wouldn't write crap like 0.0r1=0.00...001, like there's some kind of last decimal place after an infinite number of other digits. Sigh.

If one claims that 0.9r = 1, it is false in the same sense as 0.9r + 0.0r1 = 1 is false.

 

[shmoe]

If one claims that 0.9r = 1, it is false

No it isn't false. 0.9r is the limit of the sequence 0.9, 0.99, 0.999, .... In other words, it's 1, end of story. This is how a decimal is defined, it's just a convenient shorthand for an infinite series (though it becomes finite if your decimal is terminating).

..in the same sense as 0.9r + 0.0r1 = 1 is false.

This goes beyond false and enters the realm of meaningless. There is no decimal with a 1 following an infinite number of decimal places, there is no "last" decimal place.There's no smallest positive real number, no "infintessimal" real number.

 

[2inquisitive]

Just wondering:
0.9999r.... =1
0.8888r.... does not equal 0.9, correct?
0.8999r.... does this equal 0.9?
0.0999r.... does this equal 0.10? Or does such convention only apply to whole numbers? As anyone can see, I am not a mathematician, I am just curious.

 

[shmoe]

0.8888r.... does not equal 0.9, correct?

Correct, it's 8/9.

0.8999r.... does this equal 0.9?
0.0999r.... does this equal 0.10?

Yes and yes.

Or does such convention only apply to whole numbers? As anyone can see, I am not a mathematician, I am just curious.

It's not so much a convention as it is a consequence of the definition of a decimal.