Post by Eugene 2.0 on Dec 18, 2022 21:52:34 GMT
Let's say I propose a function 'f' for a certain set of things (maybe abstract, maybe not abstract). This function works the same way on each step. That means
'f(i)'≈'f(i+1)'
['≈' means 'functionally equal']. However, if to view functions not in a way most of mathematics have been always doing, but from the next angle:
f(x) → f+1(x+1)
then things go in not exact way. Firstly, let us illustrate it. Imagine we add numbers: one to one, two to two, one to two, etc. Remark that 1+1 and 2+2 are closer to each other in some sense, than 1+2 or 2+8. Also, when we add 2+3 "+" here may have one meaning, while 2654577790187+653222849's "+" may have quite different meaning; which exactly? – To get or to access more heavier numbers. In real life to multiple 8•9 is easy; not that happens in 819•331 or 14285•2771.
We see that even a simple function may hide some features in it. And that's not all what may occur. Let's have a look at this formula:
f(x) → f+i(x+j)
Unlike the previous, here any new function, which depend on their arguments, act differently, and not always as we may expect them to act. If all what we're aware of is that x≠(x+j), then all what we can say that
~['f(x)' ≈ 'f(x+j)']
So, we can't rely in any cases that our yesterday's method will work tomorrow. It might be. All twelve years you drive a van, and tomorrow it won't go. You will check all its details, deliver it to the repair mechanic garage, but they will answer you then: "Buddy, this van can never drive again". You will be staring at then, and ask: "What? Just get it worked or no paying!". But the workers are crystally honest; they just don't know why it refuses to work again. It might be.
There's no rules that rules work each day or each minute the same way.
'f(i)'≈'f(i+1)'
['≈' means 'functionally equal']. However, if to view functions not in a way most of mathematics have been always doing, but from the next angle:
f(x) → f+1(x+1)
then things go in not exact way. Firstly, let us illustrate it. Imagine we add numbers: one to one, two to two, one to two, etc. Remark that 1+1 and 2+2 are closer to each other in some sense, than 1+2 or 2+8. Also, when we add 2+3 "+" here may have one meaning, while 2654577790187+653222849's "+" may have quite different meaning; which exactly? – To get or to access more heavier numbers. In real life to multiple 8•9 is easy; not that happens in 819•331 or 14285•2771.
We see that even a simple function may hide some features in it. And that's not all what may occur. Let's have a look at this formula:
f(x) → f+i(x+j)
Unlike the previous, here any new function, which depend on their arguments, act differently, and not always as we may expect them to act. If all what we're aware of is that x≠(x+j), then all what we can say that
~['f(x)' ≈ 'f(x+j)']
So, we can't rely in any cases that our yesterday's method will work tomorrow. It might be. All twelve years you drive a van, and tomorrow it won't go. You will check all its details, deliver it to the repair mechanic garage, but they will answer you then: "Buddy, this van can never drive again". You will be staring at then, and ask: "What? Just get it worked or no paying!". But the workers are crystally honest; they just don't know why it refuses to work again. It might be.
There's no rules that rules work each day or each minute the same way.
