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Originally Posted by sonofaresiii
Well I disagree with your disagreement! So there!
edit: to explain myself a little better, no, i'm not saying f(x) = 2*x. In fact, I'm saying that's the problem-- OTHER people are saying that, but it's not true. f(x) is a function, that is f of x (f is a function of x), meaning the variable f is applied to the variable x. In our equation, we would apply 2 to 3, which in effect is multiplying it... but it's not the same as saying f(x) = f*x (though isolated, those equations are redundant). The problem is that USUALLY creating a function simply means multiplying it, so we've been trained to think that 2(3) = 2*3. But it isn't.
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Um. f(x) is literally function of x - and does not mean the variable f is applied to x.
How about functions of the form -
where the last sum is simply the first sum rewritten using the definitions
ξn =
n/
T, and Δ
ξ = (
n + 1)/
T −
n/
T = 1/
T.
Quote:
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f(x) is a function, that is f of x (f is a function of x), meaning the variable f is applied to the variable x.
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No. In the above example, there is no variable f that is applied to variable x.
The f in f(x) is simply a placeholder - for the operations that are applied to x.
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we've been trained to think that 2(3) = 2*3. But it isn't.
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We've been trained to think that way for a reason. Commutation - it comes from commutation notation and means 2*3.
Honest.
So, by direct evaluation, the equation must become 6/2*3 - as had been said before.