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Functions and Equations 
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#1
Dec1813, 08:26 AM

PF Gold
P: 41

i realize there is a similar thread here But the questions are not the same.
1.)Function is a relation but i don't know what relation exactly means. Its supposed to be a condition associating two objects but also takes in the quantitative factor in maths? 2.)Anyways, functions can be defined as equations but not all of them are expressed as equations. Can someone give me an example and state why? 3.)When one associates an element with another element, it doesn't necessarily imply equality but functions are defined as F(x) = y, where x and y are the respective elements . Doesn't this become an equation even though x and y itself are not similar things. ####But then again when the elements are numbers, i see that the function(condition) f itself becomes equal to y e.g. : let f be the condition where every value of x from R subtracted by 2. then y= x2. I thought y and x were related by f but here y = f(x)#### 


#2
Dec1813, 09:04 AM

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#3
Dec1813, 09:15 AM

PF Gold
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I have actually gone through those articles. I have read a few books and top 10 results on google but those repeat the same definition. "Function is a device. Insert Input get output."
My questions is a bit different. 


#4
Dec1813, 09:46 AM

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Functions and Equations
##f(x)=2x+1## 2x+1 is a function of x Where is input? ##f(input)=2(input)+1>Output## That's how a function normally works. 


#5
Dec1813, 09:46 AM

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Notice that, given a relation, {(x, y)}, reversing the pairs, {(y, x)}, is again a relation. If {(x, y)} is function, {(y, x)} is not necessarily a function. That is why we say a relation is "between" two sets while a function is "from" one "to" the other. {(1, 3), (2, 5), (7, 100)}. Now I can write 3= f(1), 5= f(2), and 100= f(7). But I am not going to be able to find a simple "formula", in the sense of arithmetic operations, for that function. What is true is that when we are dealing with infinite sets, we cannot just write out the pairs in the function. In order to deal with them or even talk about them, we have to have some more general way of specifying the pairs such as writing out a "formula". But that is a limitation on us, not on "functions". There exist functions so complicated we cannot write "formulas" for them but then we really cannot work with those functions so we simply ignore them. (And there are "intermediate" functions such as the "Bessel function" which is defined as the solution to "Bessel's differential equation". We cannot write this function as a formula in terms of simpler operations. We (approximately) determine its values by doing a numerical solution to the differential equation.) 


#6
Dec1913, 09:02 AM

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