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An expression in mathematics which does not have meaning and so which is not assigned an interpretation. For example, division by zero is undefined in the ...
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Defined and undefined - Wikipedia, the free encyclopedia
In mathematics, defined and undefined are used to explain whether or not expressions have meaningful, sensible, and unambiguous values. Whether an expression has a meaningful value depends on the ...
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How would this be different in mathematics than elsewhere? If a sign is undefined [i.e. if we are given no rules for using it] then we can do nothing with it, because an undefined sign is nothing more than ink marks on paper or spoken sounds; ... The Meaning of 'Undefined' and Mathematics (Waismann)
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In mathematics, defined and undefined are used to explain whether or not expressions have meaningful, sensible output. These are also known as "well-behaved" and respectively "ill-behaved". The following algebraic expressions are ... The following algebraic expressions are undefined: (see division by zero) 00 (however,
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Paradox of rich wizard and mermaid is a paradox involving infinities. It can be seen as an example that is undefined operation. Playing around undefined operation it is possible to get any wanted result. ... Complex analysis is studying the most unexpected, surprising, even paradoxical ideas in mathematics.
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In particular, IMPS supports 'quasi-equality', where a = b means 'either a and b are both undefined, or are both defined and equal'. In some parts of mathematics, this is probably the usual convention, but it has some surprising consequences, e.g. the logical equivalence x = y x - y = 0 is false for quasi-equality.
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Proof that horizontal and vertical lines are perpendicular and have undefined slope ratios. 0 * Undefined = -1. ... Axiom #4: Conversely, the slope of a vertical line is X divided by 0 (where X is non-zero) which is equal to undefined. If you need proof of this, then read this proof. Axiom #5: The final axiom is that...
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