+0  
 
0
1319
8
avatar+425 

Lets use two infinity numbers, a and b.

 

a = \(\left (1 \over 0 \right ) + 1\)

b = \(1 \over 0 \)      

 

Now we subtract them, assuming \(\left ( 1 \over 0 \right ) = ∞    \)

and \(∞ - ∞ = 0\)            

  \(b - a = \left ( ∞ + 1 \right ) - \left (∞ \right ) \\ = 1     \)

\(a - a = ∞ - ∞ \\ = 0\)

 

Simplifying yields

\(∞ - ∞ = 1 \\ ∞ - ∞ = 0 \\ 1 = 0 \\ False\)       

 

 

 

 

Hence we get \(∞ \over ∞ \\ ≠ 1\) but \(∞ \over ∞ \\ = undefined\)

Do you think this proof is valid?

 Apr 10, 2016

Best Answer 

 #5
avatar+2752 
+25

Exactly my point of saying it is indefinable

 Apr 10, 2016
 #1
avatar+6246 
+12

\(\dfrac 1 0 \text{ is undefined.}\)

 

\(\infty - \infty \text{ is meaningless, you can manipulate this to be any value you like.}\\ \\ \text{It certainly doesn't equal 0.}\)

 

\(\text{The whole "proof" is nonsense.}\)

.
 Apr 10, 2016
 #2
avatar+2752 
+10

Well, infinity plus infinity(if you were associating infinity as a number) would make a bigger number altogether, therefore making infinity indefinable. Same goes with multiplication. Everything divided by itself equals 1 so it is definable. Same with subtraction which equals 0. For the last two they could be indefinable as infinity is forever being bigger.

 Apr 10, 2016
 #3
avatar+6246 
+12

Well, infinity plus infinity(if you were associating infinity as a number) would make a bigger number altogether,

No.

 

The set of symbols

 

\(\infty + \infty > \infty\) 

 

is meaningless.  You cannot do arithmetic with infinity.

 Apr 10, 2016
 #5
avatar+2752 
+25
Best Answer

Exactly my point of saying it is indefinable

InjustaGod  Apr 10, 2016
 #8
avatar+776 
+4

yeah you can! it is used al the time! in calculus, limits, derivatives, even in the graph y=tan(x)!

User101  Apr 10, 2016
 #6
avatar+33610 
+15

Transfinite arithmetic is very non-intuitive!   See http://blog.wolframalpha.com/2010/09/10/transfinite-cardinal-arithmetic-with-wolframalpha/ for more details.

 Apr 10, 2016
 #7
avatar
+15

Infinity is a "Concept" or an " Idea"!!. You can't do math with an Idea or with Concept!!!.

 Apr 10, 2016

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