As we know, in the realms of abstract thought, such as mathematics and philosophy, infinity is that which is beyond measure and beyond grasp, while at the same time the term is limited by its very definition to being a quality of something finite.
Thus, for example, there are many things in the world, such as numbers, that may have infinity as one of their attributes and yet also be limited either in function or purpose or in their very nature.
But when we speak of the Infinite, Blessed be He, we mean the utmost of perfection and abstraction, that which encompasses everything and is beyond all possible limits.
The only thing we are permitted to say about the Infinite then, would involve the negative of all qualities.
For the Infinite is beyond anything that can be grasped in any terms-either positive or negative.
Not only is it impossible to say of the Infinite that He is in any way limited or that He is bad, one cannot even say the opposite, that He is vast or He is good.
Just as He is not matter, He is not spirit, nor can He be said to exist in any dimension meaningful to us.
The dilemma posed by this meaning of infinity is more than a consequence of the inadequacy of the human mind.
It represents a simply unbridgeable gap, a gap that cannot be crossed by anything definable.
—-Rabbi Adin Steinsaltz
From The Thirteen Petalled Rose by Rabbi Adin Steinsaltz