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What happen when q is actually o? We are taugh in school mathematics that such propositive is 'undefine', but what is it really mean by 'undefine'? To me, this is unsatisfactory answer. Perhaps people can help me clearify this matter for me.

What i accept:

Imagine a object subdivide into many equal parts, then the size of each parts approach zero.

The converse is not true.

Mathematcally, if q is a number approaching 0, but not actually 0, then s would approach infinity, which to me is a contradiction of our normal intuition. if you divide a finite size object into an infinitly fewer and fewer equal parts, each parts would approach infinity. This would mean the parts of an object is greater then the object itself. This is a contradiction of intuition, so it must not be true.

Another way to look at it is this:

If q is actually 0, then s should be p.

Intuitively specking, if an object is divide by nothing, then the result should be the object itself.