In mathematics there is defined different "Infinities of numbers" based on the idea of "1:1 matching" of sets of numbers. That is, if sets of numbers can somehow be matched on a one to one basis, they will approach the same "Infinity." Let's see what that really means by looking at one case. It is said that counting numbers, odd numbers, even numbers, and points on a line approach the same infinity. What this adds up to is if one is counting in a linear fashion, no matter how one is counting, whether by ones, twos, threes, fractions, or however, when one stops counting one has counted, within a very close limit, depending on the way it was done, everything behind. "Infinity," then, is the next point after one has stopped counting. This leads to a very practical definition of "Infinity." "Infinity" can be considered as the point beyond which one stops counting, or the point beyond which the mathematics one is using fails, or the point beyond which our equipment for examining something has a limit.

It has been said that we live between two infinities, the infinity of before when we were born and the infinity which is beyond our death. That is the space which we can, as far as we know, examine with our existence. In examining that existence, we use tools which apparently have a limit for transferring information at the speed of light, if we try to transfer information at beyond the speed of light, or attempt to examine something where we would need to transfer information at beyond the speed of light, we find ourselves blocked by the limitations of our equipment. We run into values and spaces which we call "infinite." That is, we cannot measure them by our equipment. Those values may be lost to us in "Infinity." Again, "Infinity" begins at the point just beyond our reach.

For me, that is the way I "visualize infinity," it's whatever is just out of reach of what I can do right now with what I have to work with.