Talk:Detect division by zero: Difference between revisions
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: I don't know what "mathematically incalculable" means, but I can testify that in pure mathematics, division by zero, regardless of the dividend, is undefined. Expressions such as <math>\lim_{x \to 0} \frac{x^2}{x}</math>, though they may appear to involve division by zero, actually don't. This expression, for instance, means "the number ''y'' such that for all positive ε there exists a positive δ such that for all <math>x \in (-\delta, \delta)</math>, <math>\left|\frac{x^2}{x} - y\right| < \epsilon</math>", i.e., 0. —[[User:Underscore|Underscore]] ([[User talk:Underscore|Talk]]) 01:04, 19 June 2010 (UTC) |
: I don't know what "mathematically incalculable" means, but I can testify that in pure mathematics, division by zero, regardless of the dividend, is undefined. Expressions such as <math>\lim_{x \to 0} \frac{x^2}{x}</math>, though they may appear to involve division by zero, actually don't. This expression, for instance, means "the number ''y'' such that for all positive ε there exists a positive δ such that for all <math>x \in (-\delta, \delta)</math>, <math>\left|\frac{x^2}{x} - y\right| < \epsilon</math>", i.e., 0. —[[User:Underscore|Underscore]] ([[User talk:Underscore|Talk]]) 01:04, 19 June 2010 (UTC) |
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:: According to the [http://en.wikipedia.org/wiki/Defined_and_undefined wikipedia] "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 context of the expression. For example the value of 4 − 5 is undefined if a positive integer result is required." And the problem with 0/0 is the cardinality of the result, not the lack of any results. --[[User:Rdm|Rdm]] 11:37, 19 June 2010 (UTC) |
:: According to the [http://en.wikipedia.org/wiki/Defined_and_undefined wikipedia] "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 context of the expression. For example the value of 4 − 5 is undefined if a positive integer result is required." And the problem with 0/0 is the cardinality of the result, not the lack of any results. --[[User:Rdm|Rdm]] 11:37, 19 June 2010 (UTC) |
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::: I don't know of any conventional mathematical context in which "<math>\frac{1}{0}</math>" or "<math>\frac{0}{0}</math>" has a meaningful, sensible, and unambiguous value. —[[User:Underscore|Underscore]] ([[User talk:Underscore|Talk]]) 18:42, 19 June 2010 (UTC) |
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