Mixing
Notation concerning $x rightarrow y$
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First of all, does $x rightarrow y $ have a specific name? In limits we would say " .. as $x$ approaches $y$ " .
Second point, $lim_{xrightarrow 0} 3+x=3$ if we remove the limit and just consider $3 + x$ such that $x rightarrow 0$ is it still correct to equate the operation to $3$ or should we write $3+x rightarrow 3$ (i.e $3+x = 3.0000...1$)?
If so, how should it be written? $x rightarrow 0, 3+x rightarrow 3$ ?
calculus notation
asked Feb 1 at 19:54
LuywLuyw
315
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add a comment |
$begingroup$
First of all, does $x rightarrow y $ have a specific name? In limits we would say " .. as $x$ approaches $y$ " .
Second point, $lim_{xrightarrow 0} 3+x=3$ if we remove the limit and just consider $3 + x$ such that $x rightarrow 0$ is it still correct to equate the operation to $3$ or should we write $3+x rightarrow 3$ (i.e $3+x = 3.0000...1$)?
If so, how should it be written? $x rightarrow 0, 3+x rightarrow 3$ ?
calculus notation
asked Feb 1 at 19:54
LuywLuyw
315
$endgroup$
1
$begingroup$
Depends on context, but in the context of calculus it doesn't really have a name in my experience. Borrowing from category theory notation you could perhaps call the arrow itself a limit, but I don't expect people to immediately understand in the context of calculus. For your second point, either is common in my experience. It depends on what you wish to emphasize, how obvious it is where the limit is being taken, and how familiar the reader is assumed to be with any calculations the notation may hide.
$endgroup$
– Brevan Ellefsen
Feb 1 at 20:00
$begingroup$
So it depends on situations. Thank you for your comment!
$endgroup$
– Luyw
Feb 1 at 20:14
add a comment |
$begingroup$
First of all, does $x rightarrow y $ have a specific name? In limits we would say " .. as $x$ approaches $y$ " .
Second point, $lim_{xrightarrow 0} 3+x=3$ if we remove the limit and just consider $3 + x$ such that $x rightarrow 0$ is it still correct to equate the operation to $3$ or should we write $3+x rightarrow 3$ (i.e $3+x = 3.0000...1$)?
If so, how should it be written? $x rightarrow 0, 3+x rightarrow 3$ ?
calculus notation
asked Feb 1 at 19:54
LuywLuyw
315
$endgroup$
First of all, does $x rightarrow y $ have a specific name? In limits we would say " .. as $x$ approaches $y$ " .
Second point, $lim_{xrightarrow 0} 3+x=3$ if we remove the limit and just consider $3 + x$ such that $x rightarrow 0$ is it still correct to equate the operation to $3$ or should we write $3+x rightarrow 3$ (i.e $3+x = 3.0000...1$)?
If so, how should it be written? $x rightarrow 0, 3+x rightarrow 3$ ?
calculus notation
calculus notation
asked Feb 1 at 19:54
LuywLuyw
315
asked Feb 1 at 19:54
LuywLuyw
315
edited Feb 1 at 20:14
Luyw
asked Feb 1 at 19:54
LuywLuyw
315
asked Feb 1 at 19:54
LuywLuyw
315
asked Feb 1 at 19:54
LuywLuyw
315
315
1
$begingroup$
Depends on context, but in the context of calculus it doesn't really have a name in my experience. Borrowing from category theory notation you could perhaps call the arrow itself a limit, but I don't expect people to immediately understand in the context of calculus. For your second point, either is common in my experience. It depends on what you wish to emphasize, how obvious it is where the limit is being taken, and how familiar the reader is assumed to be with any calculations the notation may hide.
$endgroup$
– Brevan Ellefsen
Feb 1 at 20:00
$begingroup$
So it depends on situations. Thank you for your comment!
$endgroup$
– Luyw
Feb 1 at 20:14
add a comment |
1
$begingroup$
Depends on context, but in the context of calculus it doesn't really have a name in my experience. Borrowing from category theory notation you could perhaps call the arrow itself a limit, but I don't expect people to immediately understand in the context of calculus. For your second point, either is common in my experience. It depends on what you wish to emphasize, how obvious it is where the limit is being taken, and how familiar the reader is assumed to be with any calculations the notation may hide.
$endgroup$
– Brevan Ellefsen
Feb 1 at 20:00
$begingroup$
So it depends on situations. Thank you for your comment!
$endgroup$
– Luyw
Feb 1 at 20:14
1
1
$begingroup$
Depends on context, but in the context of calculus it doesn't really have a name in my experience. Borrowing from category theory notation you could perhaps call the arrow itself a limit, but I don't expect people to immediately understand in the context of calculus. For your second point, either is common in my experience. It depends on what you wish to emphasize, how obvious it is where the limit is being taken, and how familiar the reader is assumed to be with any calculations the notation may hide.
$endgroup$
– Brevan Ellefsen
Feb 1 at 20:00
$begingroup$
Depends on context, but in the context of calculus it doesn't really have a name in my experience. Borrowing from category theory notation you could perhaps call the arrow itself a limit, but I don't expect people to immediately understand in the context of calculus. For your second point, either is common in my experience. It depends on what you wish to emphasize, how obvious it is where the limit is being taken, and how familiar the reader is assumed to be with any calculations the notation may hide.
$endgroup$
– Brevan Ellefsen
Feb 1 at 20:00
$begingroup$
So it depends on situations. Thank you for your comment!
$endgroup$
– Luyw
Feb 1 at 20:14
$begingroup$
So it depends on situations. Thank you for your comment!
$endgroup$
– Luyw
Feb 1 at 20:14
add a comment |
1 Answer
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$begingroup$
It is commonly written "$3+x to 3$ as $x to 0$."
answered Feb 1 at 20:20
Jon HilleryJon Hillery
707
$endgroup$
$begingroup$
Thank you for your answer!
$endgroup$
– Luyw
Feb 2 at 9:33
add a comment |
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$begingroup$
It is commonly written "$3+x to 3$ as $x to 0$."
answered Feb 1 at 20:20
Jon HilleryJon Hillery
707
$endgroup$
$begingroup$
Thank you for your answer!
$endgroup$
– Luyw
Feb 2 at 9:33
add a comment |
$begingroup$
It is commonly written "$3+x to 3$ as $x to 0$."
answered Feb 1 at 20:20
Jon HilleryJon Hillery
707
$endgroup$
$begingroup$
Thank you for your answer!
$endgroup$
– Luyw
Feb 2 at 9:33
add a comment |
$begingroup$
It is commonly written "$3+x to 3$ as $x to 0$."
answered Feb 1 at 20:20
Jon HilleryJon Hillery
707
$endgroup$
It is commonly written "$3+x to 3$ as $x to 0$."
answered Feb 1 at 20:20
Jon HilleryJon Hillery
707
answered Feb 1 at 20:20
Jon HilleryJon Hillery
707
answered Feb 1 at 20:20
Jon HilleryJon Hillery
707
answered Feb 1 at 20:20
Jon HilleryJon Hillery
707
707
$begingroup$
Thank you for your answer!
$endgroup$
– Luyw
Feb 2 at 9:33
add a comment |
$begingroup$
Thank you for your answer!
$endgroup$
– Luyw
Feb 2 at 9:33
$begingroup$
Thank you for your answer!
$endgroup$
– Luyw
Feb 2 at 9:33
$begingroup$
Thank you for your answer!
$endgroup$
– Luyw
Feb 2 at 9:33
add a comment |
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1
$begingroup$
Depends on context, but in the context of calculus it doesn't really have a name in my experience. Borrowing from category theory notation you could perhaps call the arrow itself a limit, but I don't expect people to immediately understand in the context of calculus. For your second point, either is common in my experience. It depends on what you wish to emphasize, how obvious it is where the limit is being taken, and how familiar the reader is assumed to be with any calculations the notation may hide.
$endgroup$
– Brevan Ellefsen
Feb 1 at 20:00
$begingroup$
So it depends on situations. Thank you for your comment!
$endgroup$
– Luyw
Feb 1 at 20:14