Intereting Posts

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Matrices (Hermitian and Unitary)

Possible Duplicate:

Division by $0$

I’ve always been inclined to believe that `x/0 = NaN`

is a placeholder for a character or constant that no one has created yet.

I ~~know~~ assume that none of you can tell the future, but is there an expectation that someone will eventually (successfully) define division by zero?

- Arithmetic progression
- Building the integers from scratch (and multiplying negative numbers)
- Consecutive sets of consecutive numbers which add to the same total
- Solution of $\large\binom{x}{n}+\binom{y}{n}=\binom{z}{n}$ with $n\geq 3$
- Is there a closed form of the sum $\sum _{n=1}^x\lfloor n \sqrt{2}\rfloor$
- How to show that the given equation has at least one complex root ,a s.t |a|>12

- Factorial, but with addition
- Is it possible to simulate a floor() function with elementary arithmetic?
- Why not to extend the set of natural numbers to make it closed under division by zero?
- About the addition formula $f(x+y) = f(x)g(y)+f(y)g(x)$
- negative number divided by positive number, what would be remainder?
- Understanding countable ordinals (as trees, step by step)
- Is 'no solution' the same as 'undefined'?
- subtraction of two irrational numbers to get a rational
- How can I find the square root using pen and paper?
- Is the difference of two irrationals which are each contained under a single square root irrational?

Division by zero can be defined. It is called Wheel Theory. It’s not a very popular set of mathematics and the paper that it originates from is a little difficult to find. Division by zero is left undefined in modern mathematics because it causes a loss of many useful statements. For example, $\frac{a}{b}=c \Rightarrow cb=a$. This is not true when $b=0$ and $a$ is nonzero. ($cb=0\neq a$) So, we lose generality by allowing division by zero to be defined.

Allowing division by zero also leads to proofs such as this which are valid:

$$a=b$$

$$a^2=ab$$

$$a^2-b^2=ab-b^2$$

$$(a+b)(a-b)=b(a-b)$$

$$a+b=b$$

$$2b=b$$

$$2=1$$

My understand of arithmetic division over R is this:

a/b = {x in R| b*x = a}. In case of division by 0, the answer would be none unless a = 0.

By studying the limits of the function 1/x we can tell that 1/0 is the biggest number ever(which is known to not exists :))

What I wanna say, is that 1/0 doesn’t exists and thus cannot be defined.

Unless..who knows ðŸ™‚

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