I, like all of God’s children, am a sinner. In my life, I commit infinite sins against the ideal set by God. Therefore, when I go to the Pearly Gates, Saint Peter reads my page in his book, which can fit an infinite number of sins, in a second. Therefore, he will take one second to read my sins.
In fact, though, I commit an infinite number of sins in a single day. If I live to be one hundred, over the course of my lifetime I may commit as many as 36,500 times infinity sins! Saint Peter has a trick for this issue. He can fit an infinite number of sins on one page, so he just logs them all on the same page, which he still reads in a second.
But, let’s think about it some more. God is infinite in his goodness, so every infinitesimal segment of each action I take includes infinite sins against God’s ideal. Therefore, Saint Peter has to read infinity times infinity sins against God’s ideal from his book. Impressively, Saint Peter can still do this in a second. What he in fact does is arrange a table of sins, with instants in the column header and sins in the rows header (here represented in a Google Spreadsheet). Then he reads through diagonally and finishes in a second.
However, consider that by sinning, I affect other people. When I fail to move with divine grace, it encourages other people to be lax when they move. However indirectly, each of my sins is partly to blame for every other sin that will ever be committed in the future by anyone else. Therefore, if we assume humanity will exist on into the infinite future, each sin I commit every instant cannot be accounted for fully until the infinite number of sins resulting from it are accounted for. Each of these sins cannot be accounted for until the sins resulting from each of them are accounted for. Because he cannot account for even one sin from an infinite list without accounting for an infinite number of sins, Saint Peter cannot make any amount of progress reading my sins in any amount of time.
While Peter stands trapped at his podium reading at infinite, but not uncountably infinite, speed the first sin caused by the first sin caused by my first sin in the first instant of my life, I help myself to his keys and unlock the gate. Everyone is welcome in Heaven.
Picture credit: http://thedabbler.co.uk/2015/07/how-to-approach-the-pearly-gates/