My pet philosophy is that math is real because the objects have persistent effects, like with the "if a tree falls in the forest..." riddle. Something that isn't real would be a story, because things do not have effects in it.
If a function is one-to-one, it has a (right? left? keep forgetting which one)-inverse. But if Moshe the imaginary forgot the milk, his wife may or may not shout at him, whichever way the story teller decides to take the story... So a function being one-to-one is real, but Moshe the imaginary forgetting the milk isn't.
I like this view when I'm being befuddled by a result, especially some ad absurdum argument. I tell myself: this thing is true, so if it wasn't we'd just need to look hard enough to find somewhere where two effects clash.
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My pet philosophy is that math is real because the objects have persistent effects, like with the "if a tree falls in the forest..." riddle. Something that isn't real would be a story, because things do not have effects in it.
If a function is one-to-one, it has a (right? left? keep forgetting which one)-inverse. But if Moshe the imaginary forgot the milk, his wife may or may not shout at him, whichever way the story teller decides to take the story... So a function being one-to-one is real, but Moshe the imaginary forgetting the milk isn't.
I like this view when I'm being befuddled by a result, especially some ad absurdum argument. I tell myself: this thing is true, so if it wasn't we'd just need to look hard enough to find somewhere where two effects clash.