Oops – I deleted all of Google’s data!

Dear Google,

Sorry if you lost all your data recently, it was my fault.  The Google app on my iPhone had stopped working, so I deleted it in order to reinstall.  Here’s what my iPhone asked me…

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I pressed “Delete” and in a flash it was gone, with all your data too presumably.  I must say, you seemed to restore all your data with lightning speed  – because my next Google search worked fine.  Keep up the good work.

Yours sincerely

Fin

0.9 repeater = 1 exactly

This blew my mind.  If you asked me a few days ago, I’d have said that 0.999999 (with 9′s repeating to infinity) could never exactly equal 1, since it would always be that little bit less than one.  Sure, it would tend towards one asymptotically, but it would never quite get there.  But here’s a proof someone told me to show that it does actually equal precisely one:

1/9 = 0.111111 (with 1s repeating to infinity)

Multiplying both sides by 9 gives:

1 = 0.999999 (with 9s repeating to infinity)

This seems to make much and little sense, simultaneously!  I guess infinity means an awful lot of nines.  My brain hurts.