Norman Wildberger's Five Fingered Gauntlet For Pure Mathematicians

This is part of a series Towards A Sociology of Pure Mathematics.

In 1972 Bill Gosper wrote a description of continued fraction arithmetic which represents numbers (rational, irrational and transcendental) by finitary processes which compute rational approximations to within arbitrary specified limits of accuracy. See the original paper here: Continued Fraction Arithmetic. See also Systems Thinking and Processes and Process Maths.

So it seems to me that one could take a similar view of transcendental functions. However that doesn't answer the question of whether or not the numbers or functions thus represented exist. See Hilary Putnam on Meaning and Externalism (where he gives some relevant examples) ...

... and On How Language Works With Perception To Construct The World We Live In.

Here is an on-line calculator using Gosper's rules: https://compasstech.com.au/gxwgosper

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