# Thread: zero divides zero...?

1. ## zero divides zero...?

I would argue the statement 'zero divides zero' is true.

We say '3 divides 6' because there exists an integer solution to the eaquation 3k = 6
experimental evidence suggests there is exactly one solution to the equation ie: k = 2

Similarly 'zero divides zero' is equivalent to the statement there exists an integer solution to the equation 0k = 0.
That there are many solutions for k to this equation (rather than exactly one) is not relevant because of the nature of 'there exists'

My lecturer claims 'zero divides zero' is false because 0 is specifically excluded from the definition of divides.

What say you?

2. ## Re: zero divides zero...?

The question in full is to give the answer for X_i when i = 0 for...

X_i = { x 'element_of' N | x is divisible by i }

where i is a natural number.

...maybe he is arguing 'divides' means something different to 'is divisible by'.

He is claiming the answer is the empty set but I reckon it should be {0}.