[resolved] True False - Division by zero

[WorkHorse]

Is there such an equation where n=0 returns value t=0 or otherwise returns a constant, such as t=1? t = n/n works, but 0/0 results in a divsion by zero problem. Is there an equation to get the same result without division by zero?

[jemidiah]

y=x

x=1; y=1
x=0; y=0

No division by zero needed

Did you mean to return the same constant every time?

[WorkHorse]

Return the same value for t no matter what n is, except when n is zero.

t = the equation of n

n = 1                                t = 1
n = 0.00000000000001   t = 1
n = 958.54                       t = 1
n = 65487                        t = 1
n = -1                               t = 1
n = -0.6598                      t = 1
n = -9999                         t = 1
n = -456.78                      t = 1
n = 0                                t = 0

(I can't get the spacing to match up, but you see the point.)

[dis1411]

i dont know y u dont want to use an if then statement but:

t = Abs(n <> 0)

[WorkHorse]

Originally posted by dis1411
i dont know y u dont want to use an if then statement but:

t = Abs(n <> 0)

This begs the question. What is the mathematical equation to determine n <> 0?

[dis1411]

what exactly r u trying to do?

youre not going to get it much simpler than what i gave

[WorkHorse]

I guess I am asking for the mathematical equation for NOT. How can you manually calculate that something is NOT something? Specifically, that something is NOT zero? How can I take any n and trun it to 1, unless n = 0? Is there a formula for n <> 0. Or is there NOT?

[kedaman]

WorkHorse: n <> 0 is a mathematical inequality, not an equality

[kedaman]

Originally posted by WorkHorse
Is there such an equation where n=0 returns value t=0 or otherwise returns a constant, such as t=1? t = n/n works, but 0/0 results in a divsion by zero problem. Is there an equation to get the same result without division by zero?

as for this: t=|sgn n|

[WorkHorse]

Originally posted by kedaman
WorkHorse: n <> 0 is a mathematical inequality, not an equality

Does that mean t = n <> 0 cannot be expessed more simplicity? The equation operator NOT is what it is by definition and cannot be difined by another equation?

[WorkHorse]

Originally posted by kedaman
as for this: t=|sgn n|

Brilliant. That's the ticket. Thank you.

[kedaman]

well, not is a boolean operator, and you should distinguish between boolean and aritmetic algebra

[dis1411]

ooops i was thinking in VB

[sql_lall]

Here's a little trick i used in something recently:

n*(n-1)!
----------
    n!

Note that when n =0, fraction = 0*(-1)!/0! = 0
and for all else the fraciton = 1;

I think there may be a slight problem though, as factorials aren't defined for all numbers (n must be a non-negative integer or .5 less than a non-negative integer), but i believe there is a general factorial function, which would provide what is needed.

[jemidiah]

For possibly simplifying n <> 0, the CPU's arithmetic and logic unit handles that by comparing the two numbers logically instead of using some arithmetic operations, so you'd have to find a function that happens to do what sql_lall's does to use the arithmetic method that you're after. BTW, that's pretty clever!

[sw_is_great]

There is a small problem
n*(n-1)!
----------
n!
will fail if n or (n-1) is a negative number as factorial of negative number is not defined....

-1! is not defined...

so we can use abs for that....
just a little modification :

|n|*|(n-1)|!
----------
|n|!