A lack of mathematical rigour has to do with significant gaps in arguments. Either the mathematician is being careless or is relying on intuitions that cannot be easily translated into deductive reasoning. Prior to the nineteenth century, many arguments in calculus lacked rigour. Words like’ small’, ‘infinity’, ‘approaches’, and ‘limit’ were used without ever being precisely defined. Infinite series were treated by methods analogous to those used for finite series, and no justification for doing this was offered.
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