and why does it have a beginning and an end and a middle if it’s infinite
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It kinda breaks your brain but it’s true: infinity isn’t a number. *You can always add more to infinity.* Which means there can be larger and smaller infinite sets.
Let’s say you’re the Maitre d’ at a restaurant with an infinite number of tables. And as luck would have it, an infinite number of guests have shown up and all the tables are full. Now Jennifer Aniston shows up wanting a table. What do you do?
Simple! Scootch everyone down by renumbering the tables. Table 1 is now table 2, and table 2 is table 3, and table N is now table N+1. This works into infinity; for every N there must be an N+1 so the entire infinite number of tables can be reseated. You’re worried about running into a problem at the last table? There is no last table! There’s always one more. So every N moves to N+1… the whole infinite number of them. Jen can be seated at Table 1 which is now empty.
Ok now an infinite number of Hollywood elites show up needing tables. No prob. Table N becomes Table 2N. For every N there must be a 2N, right? So now half your tables are empty: all the odd numbered tables from 1 to infinity, an infinite number of new tables to accommodate an infinite number of Hollywood stars. Now you’re making money!
The takeaway:
1. Infinity isn’t a number
2. Infinity isn’t a maximum. You can always add to it.
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