Question

Howlin

can anyone tell me if i am doing something wrong where

a/a=a
b+b=b
c=c

if a=1, b=0 and c= infinity

a/b=c
c/b=c

a/b=c/b

a=c
1=infinity


I no there is something wrong there but i cant find it
would it be that c/b does not = to c

Richard Cranium

Division by zero isn't defined or allowed in mathematics, so the expressions [latex]\frac{a}{b}[/latex] don't [latex]\frac{c}{b}[/latex] actually make any sense.

You could make anything equal to anything else ( 2=3, or 1=infinity, say) if division by zero were allowed. Your question is actually sort of an illustration of why it's not.

sponsoredwalk

Unless I'm mistaken:

Howlin wrote: »

a/a=a

[latex]\frac{a}{a} \ \neq \ a \ , \ \frac{a}{a} \ = \ 1[/latex]

Howlin wrote: »

b+b=b

[latex] b \ + \ b \ \neq \ b \ , \ b \ + \ b \ = \ 2b [/latex]

Numbers are defined so that division by zero isn't allowed,

x = y
x² = xy
x² - y² = xy - y²
x² - y² = y(x - y)
(x + y)(x - y) = y(x - y)
x + y = y
y + y = y
2y = y
2 = 1
:eek:
What's wrong here? :pac:



edit: If you're defining numbers in terms of a field then you can't have
division by zero as the axioms will show, if you define numbers like
rational numbers in terms of equivalence classes or whatever you'll
see that zero is never allowed into the domain of definition of b in
a/b. You could think of it as a ∈ Z, b ∈ N \ {0} which
means a is an integer, b is a natural number excluding zero.

Fringe

Infinity divided by something isn't equal to infinity, it just isn't defined because it's not meaningful. Same can be said for division by zero. You can't just define x/0 = infinity. This is because infinity isn't a number like 1 or 4.

bnt

You might get away with a/b=c because you can say that 1/0=∞ , but the c/b=c is just nonsensical. As already pointed out, you can't play around with ∞ as if it was a number: is ∞/0 = ∞² ? :pac: