When I was young, I used to — as an exercise — try to conceive of ∞. We would hear in Sunday School that God is Infinite, that you can’t comprehend God’s Infinite-ness.
I would imagine myself in a spaceship flying out to the edge of the universe. I would imagine all of the stuff we had left behind us, flying at the speed of imagination.
Then I would zoom out the camera, seeing that in fact we had only gotten to the edge of a tiny speck. I would recurse this and try to recurse the recursions until my brain got tired. “Infinity is so big,” I would think. “The Universe is so big. God is so big.”
All of this was on purpose. I wanted ∞ to fill up my mind. I think there are lots of religious people who do this — meditate, in a way, on ∞.
Imagining ∞ as a mathematician is easy in comparison. Using the M.O. of stereographic projection, I can conceive of infinity in an Augenblick.
Nowadays it’s up to me, whether I want to view ∞ as large or small.