Casio anomaly or gremlin or bug...

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(09-05-2017 09:08 PM)Matt Agajanian Wrote:  ... isn't mathematics predicated on accuracy and disambiguous results?
In a science as disipline and structured as mathematics, I find that it becomes confusing when this kind of ambiguity surfaces... Please clarify because this variation ... mathematics rules are flexible ...

From the PREFACE of Philosophy of Mathematics
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my emphasis
"One of the most striking features of mathematics is the fact that we are much more certain about what mathematical knowledge we have than about what mathematical knowledge is knowledge of. Mathematical knowledge is generally accepted to be more certain than any other branch of knowledge; but unlike other scientific disciplines, the subject matter of mathematics remains controversial.

In the sciences we may not be sure our theories are correct, but at least we know what it is we are studying. Physics is the study of matter and its motion within space and time. Biology is the study of living organisms and how they react and interact with their environment. Chemistry is the study of the structure of, and interactions between, the elements. When man first began speculating about the nature of the Sun and the Moon, he may not have been sure his theories were correct, but at least he could point with confidence to the objects about which he was theorizing. In all of these cases and others we know that the objects under investigation - physical matter, living organisms, the known elements, the Sun and the Moon - exist and that they are objects within the (physical) world.

In mathematics we face a different situation. Although we are all quite certain that the Pythagorean Theorem, the Prime Number Theorem, Cantor's Theorem and innumerable other theorems are true, we are much less confident about what it is to which these theorems refer. Are triangles, numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that force philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics".

I find this tome is counted among my more recurring reads.

BEST!
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