If you can count a portion of it, it is not infinite. That's why Hilbert's Hotel illustrates the contradiction.<quoted text>
Because you or anyone else believes that, or said so....doesn't make it so.
You could march up the infinite staircase , for all of your days. Never reaching the top counting , but what ever figure you count, is just a portion of an infinite sum.
If you could not count a portion of infinity, concepts like the Grand Hotel could not have been devised or written.
When you walk up your staircase, no matter how long you walk, you would be no closer to infinite steps than when you stood on the first step. That's why such a realized phenomenon is impossible.