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#Must a function be bijective in order to have an inverse function, or is injectivity enough
half mantle
stone yachtBOT
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real vector
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Technically speaking, an inverse function only exists for a bijective function. However, if a function is injective but not surjective, you can create a bijective function by restricting the range to the image of the domain.
potent kernelBOT
Unable to parse the channel name
half mantle
fuck you @potent kernel
real vector
I'm prepared to give an example.
half mantle
oh ok
real vector
Let f(x) = e^x.
Now, if we define f as from the reals to the reals, it's only injective.
half mantle
wait
ok
it's not surjective
because
f(x) can't equal 0.3534983498629693756935
for example
real vector
...no, it can.
real vector
Why do you think it can't?
half mantle
surjective means
everything in y
is mapped to by an x
what x maps to 0.3534983498629693756935
real vector
Right, and f here is not surjective, but why do you think that value in particular is not mapped to?
half mantle
because i just spammed numbers on my keyboard
real vector
...so?
half mantle
+close
real vector
Wait.
turbid girderBOT
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