i am studying real analysis from terence tao lecture notes for analysis I. http://www.math.ucla.edu/~tao/resource/general/131ah.1.03w/(adsbygoogle = window.adsbygoogle || []).push({});

from what i understand , property is just like any other statment. for example P(0.5) is P(0) with the 0s replaced with 0.5 . so the notes says (assumes ?),

##P(0.5)\textrm{ is unprovable}\Rightarrow0.5\notin N##

i mean its alright to assume something like but i just wanna make sure that what i understood is correct. if it is why not just assume something like this,

##0.5\in N\textrm{ is unprovable}\Rightarrow0.5\notin N##

but i might be wrong, so in that case could you prove 0.5 ∉ N.

thank you

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# Peano axioms for natural numbers - prove 0.5 ∉ N

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