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Indeterminate form is a mathematical expression that can obtain any value depending on circumstances. In calculus , it is usually possible to compute the limit of the sum, difference, product, quotient or power of two functions by taking the corresponding combination of the separate limits of each respective function.
[22] Knuth (1992) contends more strongly that 0 0 "has to be 1"; he draws a distinction between the value 0 0, which should equal 1, and the limiting form 0 0 (an abbreviation for a limit of f(t) g(t) where f(t), g(t) → 0), which is an indeterminate form: "Both Cauchy and Libri were right, but Libri and his defenders did not understand why ...
Isn't 0 over 0 is a determinate form because if you keep multiplying very small number very few times you just get 0. -- Taku 02:25, Nov 15, 2003 (UTC) 0/0 is indeterminate since if it had some definite value, say x, so 0x=0. But any number satisfies that equation for x, so 0/0 has no definite or determinable value.
Cancelling 0 from both sides yields =, a false statement. The fallacy here arises from the assumption that it is legitimate to cancel 0 like any other number, whereas, in fact, doing so is a form of division by 0. Using algebra, it is possible to disguise a division by zero [17] to obtain an invalid proof. For example: [18]
A fundamental property of an indeterminate is that it can be substituted with any mathematical expressions to which the same operations apply as the operations applied to the indeterminate. Some authors of abstract algebra textbooks define an indeterminate over a ring R as an element of a larger ring that is transcendental over R.
The hyperbola = /.As approaches ∞, approaches 0.. In mathematics, division by infinity is division where the divisor (denominator) is ∞.In ordinary arithmetic, this does not have a well-defined meaning, since ∞ is a mathematical concept that does not correspond to a specific number, and moreover, there is no nonzero real number that, when added to itself an infinite number of times ...
Indeterminate (variable), a symbol that is treated as a variable; Indeterminate system, a system of simultaneous equations that has more than one solution; Indeterminate equation, an equation that has more than one solution; Indeterminate form, an algebraic expression with certain limiting behaviour in mathematical analysis
In the second case, indeterminate generally indicates that a value or property can have many meaningful definitions. Additionally, it seems to be generally accepted that undefined values may not be safely used within a particular formal system, whereas indeterminate values might be, depending on the relevant rules of the particular formal ...