- #1
Loren Booda
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The multiplicative identity of the random function r(x) is any other function f(x) except where f(x)=0.
Originally posted by Loren Booda
In other words, a field in x of random values r(x) each multiplied by a corresponding value for a (non-)random mapping f(x), always retains a random mapping r(x), except where f(x)=0.
Can you imagine this situation?
Also, may this be a great way (in theory) to obtain 0's of f(x)?
Originally posted by bogdan
What if f(x)=k/r(x) ? Huh ?
Maybe you wanted to say f(r(x))...or I just don't understand...
What is returned is the property of randomness, apparently not the function itself as first defined. Indeed I need to "loosen" my definition of random r(x). Perhaps I should require its returned interval to be [-[oo],[oo]]. Thanks for your feedback.Does it always maintain the properties of the random function r(x). For example you
might have specified that if the domain is the real numbers, the function r(x)
returns values in the interval [0, 1], multiplying this by 2 does not preserve this
property.
Do you need to make your definition of randomness more tight, or am I missing
something.
The random function's universality of multiplicative identity refers to the property of the random function where the output of the function remains unchanged when multiplied by the multiplicative identity, which is typically represented as 1. In other words, when the random function is multiplied by 1, the result is the same as the original input.
The universality of multiplicative identity is important because it allows for the random function to be used in a wide range of mathematical equations and calculations. It acts as a neutral element that preserves the original input, making it a useful tool in various scientific and mathematical fields.
The universality of multiplicative identity is proven in the random function through mathematical analysis and testing. This involves using a variety of inputs and multiplying them by 1 to observe if the output remains the same. If the output does not change, it is considered to have the property of universality of multiplicative identity.
While the universality of multiplicative identity is a valuable property of the random function, it does have its limitations. For example, it only applies to the multiplication operation and does not necessarily hold true for other operations such as addition or division. Additionally, it may not hold true for certain types of random functions that have specific constraints or parameters.
The universality of multiplicative identity has many practical applications in various fields such as finance, engineering, and computer science. For example, it is used in financial modeling to determine the risk and return of investment portfolios. In computer science, it is utilized in algorithms for data encryption and compression. Overall, its universality makes it a versatile and powerful tool in solving complex problems in different industries.