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pairofstrings
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- TL;DR Summary
- Complicated and simple representation of same curve.
Thanks!
Um, could you maybe define your terms more precisely, and give some examples (using LaTeX) for what you mean?pairofstrings said:Summary:: Complicated and simple representation of same curve.
View attachment 280855If I draw some arbitrary curve then that curve can be represented convolutedly in mathematical elements and it can also be represented in simple mathematical elements?
Thanks!
Um, no.pairofstrings said:View attachment 280867
I could write the equation of the above curve by beginning with first term as x^6 and with more terms I could inch closer and closer to the precise equation of the curve - this is what I am calling convoluted equation.
Your complicated and simple in this example are subjective.pairofstrings said:Complicated:
x = 1-3+2-1+2
Simple:
x = 1
'x' can be a copy of a book.Paul Colby said:complicated and simple in this example are subjective
Your Profile Page says you are working on your BS in math. What year are you at university?pairofstrings said:View attachment 280870
How do I know if a graph is made out of complicated terms/many terms or simple terms?
Can the equation of the above curve be intricate?
Can the equation of the above curve be simple?
Can the equation for the above curve be intricated or simple?
Okay, what' the sum of Newton's Principia and Averson's "An Introduction to C*-Algebras?" Is it greater than 6?pairofstrings said:'x' can be a copy of a book.
I am self-studying. I haven't decided to go to a university. I am trying to find out what I will be doing in a university once I join it.berkeman said:Your Profile Page says you are working on your BS in math. What year are you at university?
pairofstrings said:Complicated:
x = 1-3+2-1+2
Simple:
x = 1
Paul Colby said:Okay, what' the sum of Newton's Principia and Averson's "An Introduction to C*-Algebras?" Is it greater than 6?
pairofstrings said:Why/how sum of names of two books be greater than 6?
Paul Colby said:In terms of integers, your question is we could always reduce our expressions or choose not to. Uh, okay. So what?
pairofstrings said:Complicated:
x = 1-3+2-1+2
Simple:
x = 1
As FactChecker points out the curve can be as simple as y = 1/x but what I am trying to know is if this curve can have a complicated equation; something more than just y = 1/x and I would get the same curve.FactChecker said:A gross approximation to the curve you drew is given by 1/x.
I don't know what you mean here. Do you mean that the point on the right is your current number of books?pairofstrings said:If I reduce the expression then I could know number of books in my custody.
So this is a plot of books in custody versus time?If I don't reduce the expression then I could know what happened to the books over time.
Sure. There are more complicated expressions that you might get to fit your curve better by adjusting parameters. The general shape of your curve (1/x) is a division by zero at x=0, so a better expression would probably need to have that aspect in it some way.View attachment 280920As FactChecker points out the curve can be as simple as y = 1/x but what I am trying to know is if this curve can have a complicated equation; something more than just y = 1/x and I would get the same curve.
FactChecker said:I don't know what you mean here. Do you mean that the point on the right is your current number of books?
pairofstrings said:Complicated:
x = 1-3+2-1+2
Simple:
x = 1
Paul Colby said:Your complicated and simple in this example are subjective.
No.pairofstrings said:'x' can be a copy of a book.
Again, no. This would necessarily be the net change in the number of books you have, not the total number of books you have. In other words, the 1 indicates that you now have one more book than you originally started with, which you didn't state. If you have only one book, you cannot possibly lose three books.pairofstrings said:I have one book then I lost three books then I acquired two more books then I lost one book then I acquired two more books.
Total books acquired: five.
Total books lost: four.
Total books in custody: one.
yes.pairofstrings said:If I have a curve then can its equation be complex, and also simple?
You are not "solving" this equation for x, since x is already isolated to one side. All you are doing is simplifying the not-very-complicated arithmetic expression on the right side.pairofstrings said:If I solve x = 1 - 3 + 2 - 1 + 2 then I will get number of books in my custody.
Thanks!Mark44 said:If you have only one book, you cannot possibly lose three books.
Let's get rid of all three of these words: "owe", "debt", and "lose." Instead, imagine that you are running a shop that buys and sells books.pairofstrings said:Is it correct if I replace "lose" with "owe" or "debt" in the statement I wrote?
How do I capture the notion of debt/owe/loss in a mathematical statement?
Sorry, I should have mentioned earlier that I have one book at the beginning.
Not in the scenario as I described it. To be meaningful, the seller could not sell more books at any time than there are on hand.pairofstrings said:Can 'N' also be negative??
hutchphd said:I can always make an equation more complicated. For instance y=x can be rewritten as y=(x+1)(sin^2x+cos^2x) -1.
Yes. The two equations are equivalent -- for a given value of x, both equations produce the same y value.pairofstrings said:Does y = x and y=(x+1)(sin^2x+cos^2x) -1 have the same meaning
Yes to that, also. The graphs would be exactly the same. The only difference is that the expression on the right in the 2nd equation is unsimplified.pairofstrings said:or is it the same graph but only the expressions are changing?
Mark44 said:The graphs would be exactly the same. The only difference is that the expression on the right in the 2nd equation is unsimplified.
Mark44 said:The two equations are equivalent -- for a given value of x, both equations produce the same y value.
pairofstrings said:the unsimplified 2nd equation is destined to become 'x' on simplification? Like this: y = x? Is it possible to get anything else other than 'x' on simplification from this unsimplified 2nd equation?