Brews Python 2.7.7 shows up as 2.7.5

I installed a fresh version of Python via

brew install python

Also

brew info python

tells me that it is at version 2.7.7.

I seem to remember that the python OSX Mavericks ships with is 2.5. So that

python --version

gives me 2.7.5 makes even less sense.

Also

which python
/usr/local/bin/python

should be the Homebrew version, correct?

I'm lost. Does anybody know, why my Python isn't version 2.7.7?

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You have to explicitly tell brew that you want to switch to the version of python you just installed. To do that, type:

brew switch python 2.7.7

in your command line. This may not work if the version you installed is actually 2.7.7_2. In that case, just replace 2.7.7 with 2.7.7_2 above and run it again. Once this is done, you'll have to reload your environment to pick up the changes.