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Series
Sept 17, 2020 19:18:07 GMT
Post by Eugene 2.0 on Sept 17, 2020 19:18:07 GMT
Could anyone explain me these briefly, do please?
I haven't met it in my life before, but I want to know it.
Usually, I'm fond of to get acquainted with some things which
I don't know with the help by the other people.
When we're talking about the series are we talking about the limits?
Are they the same in some sense?
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sai123
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Post by sai123 on Sept 20, 2020 1:41:12 GMT
Limits describe how a function behaves near a point, instead of at that point. This simple yet powerful idea is the basis of all of calculus.
The limit of a series is the value the series’ terms are approaching as n approaches infinty.
The series of a sequence is the sum of the sequence to a certain number of terms
I recommend you to study some precalculus and calculus topics on Khan academy and practice some problems related to that
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Series
Sept 20, 2020 5:11:13 GMT
Post by Eugene 2.0 on Sept 20, 2020 5:11:13 GMT
Limits describe how a function behaves near a point, instead of at that point. This simple yet powerful idea is the basis of all of calculus. The limit of a series is the value the series’ terms are approaching as n approaches infinty. The series of a sequence is the sum of the sequence to a certain number of terms I recommend you to study some precalculus and calculus topics on Khan academy and practice some problems related to that Aw, much grateful to you! I have already subscribed to it. And also for TrevTutor. So series are only about sum, right? Why to sum? |
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sai123
Full Member
Lifelong learner
Posts: 118
Likes: 86
Country: India
Region: Andhra pradesh
Ancestry: Globalist
Politics: Apolitical
Religion: Agnostic
Age: 18
Philosophy: Analytical
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Post by sai123 on Sept 20, 2020 10:11:39 GMT
Limits describe how a function behaves near a point, instead of at that point. This simple yet powerful idea is the basis of all of calculus. The limit of a series is the value the series’ terms are approaching as n approaches infinty. The series of a sequence is the sum of the sequence to a certain number of terms I recommend you to study some precalculus and calculus topics on Khan academy and practice some problems related to that Aw, much grateful to you! I have already subscribed to it. And also for TrevTutor. So series are only about sum, right? Why to sum? series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. |
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Post by Eugene 2.0 on Sept 20, 2020 15:00:53 GMT
Aw, much grateful to you! I have already subscribed to it. And also for TrevTutor. So series are only about sum, right? Why to sum? series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. Thank you for support and explanation. I'll try to go for some books which you've recommend. I've already had some, but the thing is I'd like to enter to all these with some other routes. It's probably not the best idea, however, if to look closely at Predicate Calculus and Propositional Logic from one side, Algebra and Calculus from the other we might see many close ideas that lay behind of them. It doesn't seem to be unsurprisingly, because logical areas have been developed by mathematicians, and not just mathematicians, but by formalists and logicists. For instance, normal forms in propositional logic are the same as sum of monomials, binomials, and polynomials (depending on what exactly the case is); the procedure of calculating functions are almost the same both in Calculus and Predicate calculus: we determine functions, check the areas of it, etc. These core ideas seem to be laid at the foundations of the ideas of the tools of mathematics (I mean algebra and calculus). I know, and I repeat myself that such a route isn't the best, or perhaps not a good idea at all. Nevertheless, to understand it - how each part in math works, - I'd prefer to move from this point. Some ideas of how to move this way I took from Jan Lukasiewitcz and Alfred Tarski's exercise books for logic. Some ideas were taken from Bertrand Russell's books of philosophy and logic. Now Internet allows us to get all this easier, however, I don't really like this way either. To quick to get the info - it's not just mine. I'd prefer to try to think at each step. Even if it takes too long time, it will be my choice. |
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sai123
Full Member
Lifelong learner
Posts: 118
Likes: 86
Country: India
Region: Andhra pradesh
Ancestry: Globalist
Politics: Apolitical
Religion: Agnostic
Age: 18
Philosophy: Analytical
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Post by sai123 on Sept 21, 2020 1:42:41 GMT
series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. Thank you for support and explanation. I'll try to go for some books which you've recommend. I've already had some, but the thing is I'd like to enter to all these with some other routes. It's probably not the best idea, however, if to look closely at Predicate Calculus and Propositional Logic from one side, Algebra and Calculus from the other we might see many close ideas that lay behind of them. It doesn't seem to be unsurprisingly, because logical areas have been developed by mathematicians, and not just mathematicians, but by formalists and logicists. For instance, normal forms in propositional logic are the same as sum of monomials, binomials, and polynomials (depending on what exactly the case is); the procedure of calculating functions are almost the same both in Calculus and Predicate calculus: we determine functions, check the areas of it, etc. These core ideas seem to be laid at the foundations of the ideas of the tools of mathematics (I mean algebra and calculus). I know, and I repeat myself that such a route isn't the best, or perhaps not a good idea at all. Nevertheless, to understand it - how each part in math works, - I'd prefer to move from this point. Some ideas of how to move this way I took from Jan Lukasiewitcz and Alfred Tarski's exercise books for logic. Some ideas were taken from Bertrand Russell's books of philosophy and logic. Now Internet allows us to get all this easier, however, I don't really like this way either. To quick to get the info - it's not just mine. I'd prefer to try to think at each step. Even if it takes too long time, it will be my choice. Yes you're right Eugene you're studying maths from different perspectives if yes then tell how did you get interested in logic? I'm curious to know about it |
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Post by Eugene 2.0 on Sept 21, 2020 5:00:11 GMT
Thank you for support and explanation. I'll try to go for some books which you've recommend. I've already had some, but the thing is I'd like to enter to all these with some other routes. It's probably not the best idea, however, if to look closely at Predicate Calculus and Propositional Logic from one side, Algebra and Calculus from the other we might see many close ideas that lay behind of them. It doesn't seem to be unsurprisingly, because logical areas have been developed by mathematicians, and not just mathematicians, but by formalists and logicists. For instance, normal forms in propositional logic are the same as sum of monomials, binomials, and polynomials (depending on what exactly the case is); the procedure of calculating functions are almost the same both in Calculus and Predicate calculus: we determine functions, check the areas of it, etc. These core ideas seem to be laid at the foundations of the ideas of the tools of mathematics (I mean algebra and calculus). I know, and I repeat myself that such a route isn't the best, or perhaps not a good idea at all. Nevertheless, to understand it - how each part in math works, - I'd prefer to move from this point. Some ideas of how to move this way I took from Jan Lukasiewitcz and Alfred Tarski's exercise books for logic. Some ideas were taken from Bertrand Russell's books of philosophy and logic. Now Internet allows us to get all this easier, however, I don't really like this way either. To quick to get the info - it's not just mine. I'd prefer to try to think at each step. Even if it takes too long time, it will be my choice. Yes you're right Eugene you're studying maths from different perspectives if yes then tell how did you get interested in logic? I'm curious to know about it Studying philosophy I took mathematical logic classes. They were inspirational, but short. I know math really not well, because during many lessons I'd rather taking nap. Without math logic philosophy doesn't seem to be a studying of something at all. For instance, there is a famous article by Gottlob Frege "Sunn and Bedeutung", where the philosopher trying to discuss what such thing as "sense" mean logically. And there is a book by Gill Deleuze, who's book "Logic of Sense" is totally senseless, except for only psychoanalytic imaginations. And if I'd choose whom to read about "sense", I wouldn't hesitate which one to pick. |
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Post by Eugene 2.0 on Sept 21, 2020 9:13:10 GMT
Thank you for support and explanation. I'll try to go for some books which you've recommend. I've already had some, but the thing is I'd like to enter to all these with some other routes. It's probably not the best idea, however, if to look closely at Predicate Calculus and Propositional Logic from one side, Algebra and Calculus from the other we might see many close ideas that lay behind of them. It doesn't seem to be unsurprisingly, because logical areas have been developed by mathematicians, and not just mathematicians, but by formalists and logicists. For instance, normal forms in propositional logic are the same as sum of monomials, binomials, and polynomials (depending on what exactly the case is); the procedure of calculating functions are almost the same both in Calculus and Predicate calculus: we determine functions, check the areas of it, etc. These core ideas seem to be laid at the foundations of the ideas of the tools of mathematics (I mean algebra and calculus). I know, and I repeat myself that such a route isn't the best, or perhaps not a good idea at all. Nevertheless, to understand it - how each part in math works, - I'd prefer to move from this point. Some ideas of how to move this way I took from Jan Lukasiewitcz and Alfred Tarski's exercise books for logic. Some ideas were taken from Bertrand Russell's books of philosophy and logic. Now Internet allows us to get all this easier, however, I don't really like this way either. To quick to get the info - it's not just mine. I'd prefer to try to think at each step. Even if it takes too long time, it will be my choice. Yes you're right Eugene you're studying maths from different perspectives if yes then tell how did you get interested in logic? I'm curious to know about it Last time I was almost completing the post as suddenly it was erased. I wanted to say some thoughts. Firstly, there are couple of books that 99.9% suit my intentions; it's Edmund Landau's "The Origins of Analysis", and "Introduction to Differential and Integral Calculus". The books were written more than a hundred years ago. The idea of them is to step bu step using logic only to determine and show how all the math operations, and number areas (Natural, Rational, etc) appeared. Even Hardy's famous exercise-book isn't so perfect. Stephen Toolmin in his "Proofs and Refutations" said that. |
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