Will you please to reopen Intuition - Countable iff Surjection iff Injection [Velleman P310 Thm 7.1.5]?
I asked this separately from my other question strictly about the proof that is now deleted. It shouln't be esteemed a duplicate, because in addition to intuition, I'm also interested in a picture. For want of organisation and focus, I didn't want to ask about all three aspects in one question.