God, the term, is just an object or person of worship. However, you are saying god is eternal. I assume he has other characteristics to in the Torah but then you say god is undefinable.
G-d is not an object or a person. G-d displays attributes, but doesn't have characteristics.
One attribute is that G-d is the First existence. Nothing precedes G-d. No matter how far back in time we go for explanations, one can always ask "What came before that?". As long as the cause is a finite cause, we can always ask 'what came before that'.
Another attribute is that G-d is Eternal, which refers to all time backwards or forwards from our human perspective. Because G-d was never brought into being, nothing can bring G-d out of being. G-d existed before Time was Created, thus logically G-d is not subject to time.
So I said you are describing someone (eternal, all powerful, for example) you cannot define. Do you see the contradiction in that statement?
No, the contradiction is in your belief that an infinite being can be defined. To be infinite is to be without borders or parameters. All human descriptions are limiting, they define what is and what is not.
Judaism teaches that there is no way that we can comprehend a reality that transcends the framework of Creation. Our very existence starts with G-d's desire (G-d doesn't really have desire, but I'm limited to human language) to create the world. However, G-d transcends the Creation. Any description that we attempt to offer of G-d will come from our human reality and therefore will be inappropriate and inaccurate.
Our sages know that we cannot comprehend G‑d in a direct manner. Accordingly, we resort to abstraction, using negative understanding. We set our limits and definitions and explain how G‑d transcends those bounds and restrictions.
If god is undefinable, how do you know he is eternal and infiniate?
This knowledge is from Torah and all our writings. G-d is termed
Bal Tachlis -- He is not bound in any way. This doesn't just mean that His powers are not limited in any way, but, more deeply, that we cannot contrast G-d with any experience known to humanity. No amount of comparison, illustration, or metaphor will bring His reality closer to our understanding. He is simply
Ein Sof -- indefinable, period.
Suppose we describe a person (e.g. Bill Gates) as being infinitely wealthy. He could never spend all he's got. But next year, his stock portfolio could grow and he would be even wealthier. That doesn't work with true infinity. You can't add anything to infinity to make it larger.
Also, if god has no definition of him whatsoever, how can you say he even exists?
G-d presented Himself to the entire nation of Israel, we had a national revelation. Although G-d is undefinable, He has created a place (the universe) in which we can interact with Him. From here (our human existence), we can perceive our relationship with G-d, as opposed to understanding G-d Himself.
Also, if god has no definition of him whatsoever, how can you say he even exists? It's like saying your friend exist on the other side of the world but you can't give her a name (I understand that), can't describe her as a human being, but still can say she has long hair and has a cheerful aura.
It seems to me that all of your writing is just crying out for a physical god. Your analogy doesn't work, since your friend is finite and has characteristics. Your friend has long hair and is cheerful. That means that your friend is not bald and is not morose. There are things that your friend isn't, so your friend isn't infinite.
G-d is everywhere and everytime.
By definition, an infinite being can not be defined.
