In mathematics, people construct and define things. And along with these, I found something very confusing:(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Being defined and existence.

**Physics Forums | Science Articles, Homework Help, Discussion**