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To Whom it May Concern:
Mathematical results are assumed to be precise. But how can mathematics be precise if results are rounded up or down? Don't such small incremental "roundings" add up to imprecision? So, in general, don't "roundings", in some way, betray the advertised precision of mathematics?
Sincerely,
Alexander

To Whom it May Concern:
Mathematical results are assumed to be precise. But how can mathematics be precise if results are rounded up or down? Don't such small incremental "roundings" add up to imprecision? So, in general, don't "roundings", in some way, betray the advertised precision of mathematics?
Sincerely,
Alexander

Response from Douglas Burnham on :

'Mathematics' covers a lot of ground: from pure geometry, for example, which is not quantitative at all -- that is to say, is not concerned with numbers and calculations -- to statistics which is not only quantitative but must do some version of the 'rounding' you speak of. Within statistics, however, part of the science (and in fact perhaps the most important part of the science!) is its ability to describe the imprecision of its results. For example, with the notion of a 'confidence interval'. This has two implications, it seems to me, one practical and one theoretical. First, the way in which statistical results are distributed through non-scientific forms of publication (reported in Newspapers, for example) often leaves out this analysis of precision, and every result is reported with equal confidence. This is not precisely a philosophical problem, to be sure, but certainly has implications for the ethics of the media, and for how scientific research is translated into political...