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Full Idea
One of the motivations behind Cantor's and Dedekind's pioneering explorations in the field was the ambition to give real analysis a new foundation in set theory - and hence a foundation independent of geometry.
Gist of Idea
Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry)
Source
Ian Rumfitt (The Boundary Stones of Thought [2015], 9.6)
Book Ref
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.298
A Reaction
Rumfitt is inclined to think that the project has failed, although a weaker set theory than ZF might do the job (within limits).