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How to interpret objects and symbols in written mathematics?
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When reading mathematics how do you intuitively interpret the given objects such as sets, functions, sequences, etc? do you automatically visualize them graphically?
When dealing with sets $A, B, X, Y$ do you think of them represented as venn diagrams?
And whenever you come across functions $f:Xrightarrow{Y}$ given by some formula for $f(x)$, and for sequences $a_n:mathbb{N} rightarrow mathbb{R}$ given by some formula for $a_n$, do you interpret $f(x)$ and $a_n$ as the points along the vertical axis?
I am self-studying Real Analysis and would like to be able to represent the given information in a more beneficial way rather than just memorizing symbols.
soft-question advice
asked Feb 1 at 15:00
AdnaanAdnaan
506
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add a comment |
$begingroup$
When reading mathematics how do you intuitively interpret the given objects such as sets, functions, sequences, etc? do you automatically visualize them graphically?
When dealing with sets $A, B, X, Y$ do you think of them represented as venn diagrams?
And whenever you come across functions $f:Xrightarrow{Y}$ given by some formula for $f(x)$, and for sequences $a_n:mathbb{N} rightarrow mathbb{R}$ given by some formula for $a_n$, do you interpret $f(x)$ and $a_n$ as the points along the vertical axis?
I am self-studying Real Analysis and would like to be able to represent the given information in a more beneficial way rather than just memorizing symbols.
soft-question advice
asked Feb 1 at 15:00
AdnaanAdnaan
506
$endgroup$
2
$begingroup$
There is no single answer, it depends on context. Some problems are better addressed graphically, and for others this is of no help or is just impossible.
$endgroup$
– Yves Daoust
Feb 1 at 15:29
1
$begingroup$
Venn diagrams are handy for three sets but not more. Karnaugh tables remain practical up to six sets.
$endgroup$
– Yves Daoust
Feb 1 at 15:34
add a comment |
$begingroup$
When reading mathematics how do you intuitively interpret the given objects such as sets, functions, sequences, etc? do you automatically visualize them graphically?
When dealing with sets $A, B, X, Y$ do you think of them represented as venn diagrams?
And whenever you come across functions $f:Xrightarrow{Y}$ given by some formula for $f(x)$, and for sequences $a_n:mathbb{N} rightarrow mathbb{R}$ given by some formula for $a_n$, do you interpret $f(x)$ and $a_n$ as the points along the vertical axis?
I am self-studying Real Analysis and would like to be able to represent the given information in a more beneficial way rather than just memorizing symbols.
soft-question advice
asked Feb 1 at 15:00
AdnaanAdnaan
506
$endgroup$
When reading mathematics how do you intuitively interpret the given objects such as sets, functions, sequences, etc? do you automatically visualize them graphically?
When dealing with sets $A, B, X, Y$ do you think of them represented as venn diagrams?
And whenever you come across functions $f:Xrightarrow{Y}$ given by some formula for $f(x)$, and for sequences $a_n:mathbb{N} rightarrow mathbb{R}$ given by some formula for $a_n$, do you interpret $f(x)$ and $a_n$ as the points along the vertical axis?
I am self-studying Real Analysis and would like to be able to represent the given information in a more beneficial way rather than just memorizing symbols.
soft-question advice
soft-question advice
asked Feb 1 at 15:00
AdnaanAdnaan
506
asked Feb 1 at 15:00
AdnaanAdnaan
506
edited Feb 1 at 15:25
Adnaan
asked Feb 1 at 15:00
AdnaanAdnaan
506
asked Feb 1 at 15:00
AdnaanAdnaan
506
asked Feb 1 at 15:00
AdnaanAdnaan
506
506
2
$begingroup$
There is no single answer, it depends on context. Some problems are better addressed graphically, and for others this is of no help or is just impossible.
$endgroup$
– Yves Daoust
Feb 1 at 15:29
1
$begingroup$
Venn diagrams are handy for three sets but not more. Karnaugh tables remain practical up to six sets.
$endgroup$
– Yves Daoust
Feb 1 at 15:34
add a comment |
2
$begingroup$
There is no single answer, it depends on context. Some problems are better addressed graphically, and for others this is of no help or is just impossible.
$endgroup$
– Yves Daoust
Feb 1 at 15:29
1
$begingroup$
Venn diagrams are handy for three sets but not more. Karnaugh tables remain practical up to six sets.
$endgroup$
– Yves Daoust
Feb 1 at 15:34
2
2
$begingroup$
There is no single answer, it depends on context. Some problems are better addressed graphically, and for others this is of no help or is just impossible.
$endgroup$
– Yves Daoust
Feb 1 at 15:29
$begingroup$
There is no single answer, it depends on context. Some problems are better addressed graphically, and for others this is of no help or is just impossible.
$endgroup$
– Yves Daoust
Feb 1 at 15:29
1
1
$begingroup$
Venn diagrams are handy for three sets but not more. Karnaugh tables remain practical up to six sets.
$endgroup$
– Yves Daoust
Feb 1 at 15:34
$begingroup$
Venn diagrams are handy for three sets but not more. Karnaugh tables remain practical up to six sets.
$endgroup$
– Yves Daoust
Feb 1 at 15:34
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Most notation is contextual. Here is a rough standard:
$require{amsmath}$
begin{align}
&i,j,k,l,m,n,pldots&text{integers}\
&p,q,r,s,tldots&text{real numbers}\
&mathbb{C},mathbb{R},mathbb{Q},mathbb{Z},mathbb{N}ldots&text{sets of numbers}\
&X,Y,W,Z,Omega,Gamma,Lambdaldots&text{main sets---e.g., linear spaces}\
&A,B,C,U,V,S,Tldots&text{subsets of main sets}\
&a,b,x,y,z,alpha,beta,lambda,mu,omegaldots&text{elements of sets}\
&mathcal{A},mathcal{B},mathcal{C}ldots&text{sets of sets---e.g., filters, topologies}\
&f,g,h,p,q,alpha,beta,lambda,mu,pildots&text{functions}\
&Gamma,Delta,Phi,Psildots&text{sets of functions}
end{align}
As for your question, think about how you would go about teaching the very thing you are reading. Then you will see the utility of notation. Furthermore, you will have a better understanding of why the author of the written material chose to write things in a certain way (maybe not the best way, in your opinion). It is up to you to rewrite things you would like to memorize in your own language with the caveat that likely others will dislike your own language and that some translation may be required when speaking to others.
I want to conclude that it is very important that mathematicians be allowed to have their own unique perspective and visualization. It is fine to ask how others visualize, but feel free to attempt to create your own visualization and run with it.
answered Feb 1 at 15:12
Alberto TakaseAlberto Takase
2,378719
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add a comment |
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1 Answer
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1 Answer
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$begingroup$
Most notation is contextual. Here is a rough standard:
$require{amsmath}$
begin{align}
&i,j,k,l,m,n,pldots&text{integers}\
&p,q,r,s,tldots&text{real numbers}\
&mathbb{C},mathbb{R},mathbb{Q},mathbb{Z},mathbb{N}ldots&text{sets of numbers}\
&X,Y,W,Z,Omega,Gamma,Lambdaldots&text{main sets---e.g., linear spaces}\
&A,B,C,U,V,S,Tldots&text{subsets of main sets}\
&a,b,x,y,z,alpha,beta,lambda,mu,omegaldots&text{elements of sets}\
&mathcal{A},mathcal{B},mathcal{C}ldots&text{sets of sets---e.g., filters, topologies}\
&f,g,h,p,q,alpha,beta,lambda,mu,pildots&text{functions}\
&Gamma,Delta,Phi,Psildots&text{sets of functions}
end{align}
As for your question, think about how you would go about teaching the very thing you are reading. Then you will see the utility of notation. Furthermore, you will have a better understanding of why the author of the written material chose to write things in a certain way (maybe not the best way, in your opinion). It is up to you to rewrite things you would like to memorize in your own language with the caveat that likely others will dislike your own language and that some translation may be required when speaking to others.
I want to conclude that it is very important that mathematicians be allowed to have their own unique perspective and visualization. It is fine to ask how others visualize, but feel free to attempt to create your own visualization and run with it.
answered Feb 1 at 15:12
Alberto TakaseAlberto Takase
2,378719
$endgroup$
add a comment |
$begingroup$
Most notation is contextual. Here is a rough standard:
$require{amsmath}$
begin{align}
&i,j,k,l,m,n,pldots&text{integers}\
&p,q,r,s,tldots&text{real numbers}\
&mathbb{C},mathbb{R},mathbb{Q},mathbb{Z},mathbb{N}ldots&text{sets of numbers}\
&X,Y,W,Z,Omega,Gamma,Lambdaldots&text{main sets---e.g., linear spaces}\
&A,B,C,U,V,S,Tldots&text{subsets of main sets}\
&a,b,x,y,z,alpha,beta,lambda,mu,omegaldots&text{elements of sets}\
&mathcal{A},mathcal{B},mathcal{C}ldots&text{sets of sets---e.g., filters, topologies}\
&f,g,h,p,q,alpha,beta,lambda,mu,pildots&text{functions}\
&Gamma,Delta,Phi,Psildots&text{sets of functions}
end{align}
As for your question, think about how you would go about teaching the very thing you are reading. Then you will see the utility of notation. Furthermore, you will have a better understanding of why the author of the written material chose to write things in a certain way (maybe not the best way, in your opinion). It is up to you to rewrite things you would like to memorize in your own language with the caveat that likely others will dislike your own language and that some translation may be required when speaking to others.
I want to conclude that it is very important that mathematicians be allowed to have their own unique perspective and visualization. It is fine to ask how others visualize, but feel free to attempt to create your own visualization and run with it.
answered Feb 1 at 15:12
Alberto TakaseAlberto Takase
2,378719
$endgroup$
add a comment |
$begingroup$
Most notation is contextual. Here is a rough standard:
$require{amsmath}$
begin{align}
&i,j,k,l,m,n,pldots&text{integers}\
&p,q,r,s,tldots&text{real numbers}\
&mathbb{C},mathbb{R},mathbb{Q},mathbb{Z},mathbb{N}ldots&text{sets of numbers}\
&X,Y,W,Z,Omega,Gamma,Lambdaldots&text{main sets---e.g., linear spaces}\
&A,B,C,U,V,S,Tldots&text{subsets of main sets}\
&a,b,x,y,z,alpha,beta,lambda,mu,omegaldots&text{elements of sets}\
&mathcal{A},mathcal{B},mathcal{C}ldots&text{sets of sets---e.g., filters, topologies}\
&f,g,h,p,q,alpha,beta,lambda,mu,pildots&text{functions}\
&Gamma,Delta,Phi,Psildots&text{sets of functions}
end{align}
As for your question, think about how you would go about teaching the very thing you are reading. Then you will see the utility of notation. Furthermore, you will have a better understanding of why the author of the written material chose to write things in a certain way (maybe not the best way, in your opinion). It is up to you to rewrite things you would like to memorize in your own language with the caveat that likely others will dislike your own language and that some translation may be required when speaking to others.
I want to conclude that it is very important that mathematicians be allowed to have their own unique perspective and visualization. It is fine to ask how others visualize, but feel free to attempt to create your own visualization and run with it.
answered Feb 1 at 15:12
Alberto TakaseAlberto Takase
2,378719
$endgroup$
Most notation is contextual. Here is a rough standard:
$require{amsmath}$
begin{align}
&i,j,k,l,m,n,pldots&text{integers}\
&p,q,r,s,tldots&text{real numbers}\
&mathbb{C},mathbb{R},mathbb{Q},mathbb{Z},mathbb{N}ldots&text{sets of numbers}\
&X,Y,W,Z,Omega,Gamma,Lambdaldots&text{main sets---e.g., linear spaces}\
&A,B,C,U,V,S,Tldots&text{subsets of main sets}\
&a,b,x,y,z,alpha,beta,lambda,mu,omegaldots&text{elements of sets}\
&mathcal{A},mathcal{B},mathcal{C}ldots&text{sets of sets---e.g., filters, topologies}\
&f,g,h,p,q,alpha,beta,lambda,mu,pildots&text{functions}\
&Gamma,Delta,Phi,Psildots&text{sets of functions}
end{align}
As for your question, think about how you would go about teaching the very thing you are reading. Then you will see the utility of notation. Furthermore, you will have a better understanding of why the author of the written material chose to write things in a certain way (maybe not the best way, in your opinion). It is up to you to rewrite things you would like to memorize in your own language with the caveat that likely others will dislike your own language and that some translation may be required when speaking to others.
I want to conclude that it is very important that mathematicians be allowed to have their own unique perspective and visualization. It is fine to ask how others visualize, but feel free to attempt to create your own visualization and run with it.
answered Feb 1 at 15:12
Alberto TakaseAlberto Takase
2,378719
edited Feb 1 at 15:25
answered Feb 1 at 15:12
Alberto TakaseAlberto Takase
2,378719
answered Feb 1 at 15:12
Alberto TakaseAlberto Takase
2,378719
answered Feb 1 at 15:12
Alberto TakaseAlberto Takase
2,378719
2,378719
add a comment |
add a comment |
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$begingroup$
There is no single answer, it depends on context. Some problems are better addressed graphically, and for others this is of no help or is just impossible.
$endgroup$
– Yves Daoust
Feb 1 at 15:29
1
$begingroup$
Venn diagrams are handy for three sets but not more. Karnaugh tables remain practical up to six sets.
$endgroup$
– Yves Daoust
Feb 1 at 15:34