In mathematics, people construct and define things. And along with these, I found something very confusing: Statement 1: if a thing exists, then the thing is defined. I think this statement is true in mathematics. But this kind of statement I can't translate to first order calculus. Anyway, if this is true, then it is also ture: Statement 2: if a thing is not defined, then the thing does not exists. Then here a confusion begins: Example 1: We know that 6/0 is undefined (at least, most people say so). So by Statement 2 we may derive that 6/0 does not exists. Well, I'm not sure if it is true... Suppose 6/0 is a number such that multyplying this with 9 produces 6. In a first thought, if I think 6/0 like this, then it treuly does not exists. But In this first thought, I kinda already defined what 6/0 is, which means, 6/0 is defined. If I don suppose 6/0 like that, I have no idea of what this is, thus I can't think of the existence of it at all. Example 2: Now, if you consider some strange symbol like (6,0)/0, then it is undefined. But in the first place, I don't think I can say of whether it exists or not at all, because I do not know what this is. Question: (1) Maybe, Statement 1 is wrong in the first place. Is it? Please correct me. (2) If it is ture, where I am wrong? Is my notion of 'being defined' wrong? Please give me insight.