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Feb
5
comment Book on foundational reasoning of standard arithmetics “curriculum”
One last question. Why e,g in this thread they seem to suggest that PM is extremely difficult to read even for professionals? math.stackexchange.com/questions/813119/…
Feb
5
comment Book on foundational reasoning of standard arithmetics “curriculum”
My intent was that I am interested in a book with specific focus so that it is "practical" and not something that covers pages over philosophical notions that covers things about all aspects of mathematics. Does that make sense?
Feb
5
comment Book on foundational reasoning of standard arithmetics “curriculum”
I'll start that book (along with the others mentioned). Concerning you I don't know what you are looking for, in case it helps: My interest was in a book that covers the basic arithmetics that we fundamentally use every day (logarithms, ratios, series, fractions, basic operations) but instead of just the formulas (which we all know by heart) an intuitive reasoning. When I meant not too much formal, perhaps I used the wrong term.
Feb
5
comment Book on foundational reasoning of standard arithmetics “curriculum”
To be honest I don't understand what you are trying to convey with your answer. You seem to suggest that my question is pointless since there is a school that supports that logic and math are separated. I assume you are suggesting to read Principia Mathematica but what background does this book require? Can a muddleheaded person readily read it?
Feb
4
comment Book on foundational reasoning of standard arithmetics “curriculum”
What do you mean that the foundation of mathematics do not lie in logic? Don't we use logic rules to form proofs?
Feb
3
comment Book on foundational reasoning of standard arithmetics “curriculum”
I am interested more in topics like: logarithms, ratios, series, fractions, basic operations i.e. all the basic topics of classic arithmetic. When I mean less formality I mean that I would prefer to not be too abstract in a way that is not practical. If something exists that is good but is formal I am fine with that if there is nothing else.
Feb
3
comment Book on foundational reasoning of standard arithmetics “curriculum”
@RobArthan:No I was asking because the title says "Analysis". I am trying to understand if it is about arithmetics
Feb
3
comment Book on foundational reasoning of standard arithmetics “curriculum”
@David:What exactly is the target of Landau's book?
Feb
3
comment Book on foundational reasoning of standard arithmetics “curriculum”
But how is set theory related to the type of book I am asking about? May be I am missing something here?
Feb
3
comment Book on foundational reasoning of standard arithmetics “curriculum”
But isn't this book only focusing on the idea of what is a number?
Feb
3
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Feb
3
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Feb
3
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Feb
3
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Feb
3
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Oct
3
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Sep
7
comment Not clear on what we mean with numbers with infinite digits
But 1/2=3/6=0.5 While 6/3=2 vs 6*(1/3) = 1.999999.. =~ 2
Sep
7
comment Not clear on what we mean with numbers with infinite digits
Yes but 6/3=2 not 1.9998. So how come with 2 different ways we get exactly 2 and we approach 2?
Sep
7
comment Not clear on what we mean with numbers with infinite digits
...means the limit of the sequence of rational numbers: I am ashamed to say I don't understand this part TBH
Sep
7
comment Not clear on what we mean with numbers with infinite digits
But then why doesn't 1.99999999... equal to 1.88888888.... and then 2 equals 1.8888888888 for 1.8888.... and 1.777777....>