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Is there a proof for why: 1 + 1 = 2 I've heard of the Principua Mathematica, and that it came close but never fully did it.

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On the contrary, they do prove it.
whats the sense of 2 if its not 1+1
2-1=1 and so 1+1=2

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I heard that they came close but never defined addition; after them godel came along and made things even more complicated.
You have to put that book in its historical context and the "project" that Russell and Whitehead were undertaking. Given their very careful definition of number, and definition of 1, and definition of 2, and definition of +, and definition of =, then do indeed show that 1 + 1 = 2. What they didn't do, and what Gödel's results cemented, is finish building up mathematics from elementary logical definitions.
Thank you, that cleared it up
Among other things, I've read a graphic novel about this ... let me find it ...
If you want a relatively digestible accounting of the story, this isn't a bad resource.
thanks, it'll be useful. Until i'm one day ready to even attempt reading principua mathematica.
It's a bit of a historical curiosity now. If you're interested in Russell's definition of number, a much shorter and in many ways more useful book is this:

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