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> We all grew up learning math before programming, and mathematically speaking, there is no qualitative difference between 15 and 14.7 IMO, there is a huge qua

> We all grew up learning math before programming, and mathematically speaking, there is no qualitative difference between 15 and 14.7 IMO, there is a huge qualitative difference between 15 and 14.7; 15 is an integer, while 14.7 isn’t. I also think most people would know that instinctively. Reason? I think most people learn arithmetic progressing more or less along these lines: - positive integers - non-negative integers (i.e. learning and understanding the concept of ‘zero’) - non-negative rationals - all rationals - decimal fractions - all reals Phrased another way: I would think the majority of people would learn to count to 15 long before learning what 14.7 means. Also, as sfpotter already said, switching to doubles only isn’t a panacea. Neither are bigints (won’t help representing the result of ⅓ exactly, for example), rationals (won’t help representing the typical hypothenuse of a triangle exactly, for example), or radicals (won’t help computing the area of a unit circle exactly) A CAS would help, but by then, you’re giving up lots and lots of performance. (that doesn’t mean I am a fan of languages that silently round integer division. Silently moving to bigints and rationals IMO can be a good choice, but silently moving from an exact type to an inexact one IMO never is)

zoky 3y ago
> IMO, there is a huge qualitative difference between 15 and 14.7; 15 is an integer, while 14.7 isn’t. Yes and no. The fact that one is an integer and one isn’t only really matters when considering them in the context of a set, e.g. when counting. But there’s nothing special about integers that affects how we use them relative to decimals. Multiply both of them by 10, and you’re back to integers. Divide them both by 10, and you’ve got decimals. It’s perfectly reasonably for all mathematical purposes to consider 15 and 15.0 to be equivalent to each other. This isn’t the case with computers, and that has nothing to do with mathematics.

zoky 3y ago

> IMO, there is a huge qualitative difference between 15 and 14.7; 15 is an integer, while 14.7 isn’t. Yes and no. The fact that one is an integer and one isn’t only really matters when considering them in the context of a set, e.g. when counting. But there’s nothing special about integers that affects how we use them relative to decimals. Multiply both of them by 10, and you’re back to integers. Divide them both by 10, and you’ve got decimals. It’s perfectly reasonably for all mathematical purposes to consider 15 and 15.0 to be equivalent to each other. This isn’t the case with computers, and that has nothing to do with mathematics.