equal spacing for 'ordinary' limit and one-sided limit
The problem is that one-sided limits have subscripted symbols above $a$. I tried adding a blank subscript to the 'ordinary' limit, but that didn't seem to even out spacing.
underline{Theorem:} $lim limits_{x to a^{}} f(x)
Longleftrightarrow lim limits_{x to a^{-}} f(x)
= lim limits_{x to a^{+}} f(x)$
amsmath
asked Dec 18 '18 at 15:21
Miguel Cumming-Romo
363
add a comment |
The problem is that one-sided limits have subscripted symbols above $a$. I tried adding a blank subscript to the 'ordinary' limit, but that didn't seem to even out spacing.
underline{Theorem:} $lim limits_{x to a^{}} f(x)
Longleftrightarrow lim limits_{x to a^{-}} f(x)
= lim limits_{x to a^{+}} f(x)$
amsmath
asked Dec 18 '18 at 15:21
Miguel Cumming-Romo
363
2
You would use a "phantom" glyph, as inlimits_{x to a^{phantom{-}}}to leave extra space in the ordinary limit, but I don't like the look of it at all.
– Steven B. Segletes
Dec 18 '18 at 15:31
A bit off-topic, but it seems like you are missing the word "exists".
– Andreas Rejbrand
Dec 18 '18 at 19:52
add a comment |
The problem is that one-sided limits have subscripted symbols above $a$. I tried adding a blank subscript to the 'ordinary' limit, but that didn't seem to even out spacing.
underline{Theorem:} $lim limits_{x to a^{}} f(x)
Longleftrightarrow lim limits_{x to a^{-}} f(x)
= lim limits_{x to a^{+}} f(x)$
amsmath
asked Dec 18 '18 at 15:21
Miguel Cumming-Romo
363
The problem is that one-sided limits have subscripted symbols above $a$. I tried adding a blank subscript to the 'ordinary' limit, but that didn't seem to even out spacing.
underline{Theorem:} $lim limits_{x to a^{}} f(x)
Longleftrightarrow lim limits_{x to a^{-}} f(x)
= lim limits_{x to a^{+}} f(x)$
amsmath
amsmath
asked Dec 18 '18 at 15:21
Miguel Cumming-Romo
363
asked Dec 18 '18 at 15:21
Miguel Cumming-Romo
363
edited Dec 18 '18 at 16:24
asked Dec 18 '18 at 15:21
Miguel Cumming-Romo
363
asked Dec 18 '18 at 15:21
Miguel Cumming-Romo
363
asked Dec 18 '18 at 15:21
Miguel Cumming-Romo
363
363
2
You would use a "phantom" glyph, as inlimits_{x to a^{phantom{-}}}to leave extra space in the ordinary limit, but I don't like the look of it at all.
– Steven B. Segletes
Dec 18 '18 at 15:31
A bit off-topic, but it seems like you are missing the word "exists".
– Andreas Rejbrand
Dec 18 '18 at 19:52
add a comment |
2
You would use a "phantom" glyph, as inlimits_{x to a^{phantom{-}}}to leave extra space in the ordinary limit, but I don't like the look of it at all.
– Steven B. Segletes
Dec 18 '18 at 15:31
A bit off-topic, but it seems like you are missing the word "exists".
– Andreas Rejbrand
Dec 18 '18 at 19:52
2
2
You would use a "phantom" glyph, as in
limits_{x to a^{phantom{-}}} to leave extra space in the ordinary limit, but I don't like the look of it at all.– Steven B. Segletes
Dec 18 '18 at 15:31
You would use a "phantom" glyph, as in
limits_{x to a^{phantom{-}}} to leave extra space in the ordinary limit, but I don't like the look of it at all.– Steven B. Segletes
Dec 18 '18 at 15:31
A bit off-topic, but it seems like you are missing the word "exists".
– Andreas Rejbrand
Dec 18 '18 at 19:52
A bit off-topic, but it seems like you are missing the word "exists".
– Andreas Rejbrand
Dec 18 '18 at 19:52
add a comment |
3 Answers
3
active
oldest
votes
Use vphantom{+} to have the same height as the RHS.
underline{Theorem:} $limlimits_{x to a^{vphantom{+}}} f(x)
Longleftrightarrow limlimits_{x to a^{-}} f(x)
= limlimits_{x to a^{+}} f(x)$
answered Dec 18 '18 at 15:33
AboAmmar
33.1k22882
add a comment |
Here's a possibility, but takes a lot of work to get there. It uses the vphantom mentioned by AboAmmar, but it also horizontally centers the to under the lim.
It does it by placing a phantom scripted - to the left of the one-sided limits. But then it must also introduce !!! negative space to compensate.
documentclass{article}
begin{document}
underline{Theorem:} $lim limits_{x to a^{vphantom{-}}} f(x)
Longleftrightarrow !!!lim limits_{^{phantom{-}}x to a^{-}} f(x)
= !!!lim limits_{^{phantom{-}}x to a^{+}} f(x)$
end{document}
answered Dec 18 '18 at 15:37
Steven B. Segletes
152k9193400
add a comment |
If a is a constant, I'd suggest you use uparrow and downarrow to indicate unambiguously that the x is supposed to approach a from below and above, respectively. A very nice side-effect of this notation is that xuparrow a and xdownarrow a take up less space than xto a -- obviating any need to make spacing adjustments.
If, in addition, you wish to assure that xto a and xuparrow a (and xdownarrow a) are typeset at same distance below "lim", just change xto a to xto avphantom{uparrow}.
documentclass{article}
begin{document}
$displaystyle
lim_{xto a} f(x)Longleftrightarrow
lim_{xuparrow a} f(x)=
lim_{xdownarrow a} f(x)$
end{document}
answered Dec 18 '18 at 16:36
Mico
273k30369756
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
Use vphantom{+} to have the same height as the RHS.
underline{Theorem:} $limlimits_{x to a^{vphantom{+}}} f(x)
Longleftrightarrow limlimits_{x to a^{-}} f(x)
= limlimits_{x to a^{+}} f(x)$
answered Dec 18 '18 at 15:33
AboAmmar
33.1k22882
add a comment |
Use vphantom{+} to have the same height as the RHS.
underline{Theorem:} $limlimits_{x to a^{vphantom{+}}} f(x)
Longleftrightarrow limlimits_{x to a^{-}} f(x)
= limlimits_{x to a^{+}} f(x)$
answered Dec 18 '18 at 15:33
AboAmmar
33.1k22882
add a comment |
Use vphantom{+} to have the same height as the RHS.
underline{Theorem:} $limlimits_{x to a^{vphantom{+}}} f(x)
Longleftrightarrow limlimits_{x to a^{-}} f(x)
= limlimits_{x to a^{+}} f(x)$
answered Dec 18 '18 at 15:33
AboAmmar
33.1k22882
Use vphantom{+} to have the same height as the RHS.
underline{Theorem:} $limlimits_{x to a^{vphantom{+}}} f(x)
Longleftrightarrow limlimits_{x to a^{-}} f(x)
= limlimits_{x to a^{+}} f(x)$
answered Dec 18 '18 at 15:33
AboAmmar
33.1k22882
answered Dec 18 '18 at 15:33
AboAmmar
33.1k22882
answered Dec 18 '18 at 15:33
AboAmmar
33.1k22882
answered Dec 18 '18 at 15:33
AboAmmar
33.1k22882
33.1k22882
add a comment |
add a comment |
Here's a possibility, but takes a lot of work to get there. It uses the vphantom mentioned by AboAmmar, but it also horizontally centers the to under the lim.
It does it by placing a phantom scripted - to the left of the one-sided limits. But then it must also introduce !!! negative space to compensate.
documentclass{article}
begin{document}
underline{Theorem:} $lim limits_{x to a^{vphantom{-}}} f(x)
Longleftrightarrow !!!lim limits_{^{phantom{-}}x to a^{-}} f(x)
= !!!lim limits_{^{phantom{-}}x to a^{+}} f(x)$
end{document}
answered Dec 18 '18 at 15:37
Steven B. Segletes
152k9193400
add a comment |
Here's a possibility, but takes a lot of work to get there. It uses the vphantom mentioned by AboAmmar, but it also horizontally centers the to under the lim.
It does it by placing a phantom scripted - to the left of the one-sided limits. But then it must also introduce !!! negative space to compensate.
documentclass{article}
begin{document}
underline{Theorem:} $lim limits_{x to a^{vphantom{-}}} f(x)
Longleftrightarrow !!!lim limits_{^{phantom{-}}x to a^{-}} f(x)
= !!!lim limits_{^{phantom{-}}x to a^{+}} f(x)$
end{document}
answered Dec 18 '18 at 15:37
Steven B. Segletes
152k9193400
add a comment |
Here's a possibility, but takes a lot of work to get there. It uses the vphantom mentioned by AboAmmar, but it also horizontally centers the to under the lim.
It does it by placing a phantom scripted - to the left of the one-sided limits. But then it must also introduce !!! negative space to compensate.
documentclass{article}
begin{document}
underline{Theorem:} $lim limits_{x to a^{vphantom{-}}} f(x)
Longleftrightarrow !!!lim limits_{^{phantom{-}}x to a^{-}} f(x)
= !!!lim limits_{^{phantom{-}}x to a^{+}} f(x)$
end{document}
answered Dec 18 '18 at 15:37
Steven B. Segletes
152k9193400
Here's a possibility, but takes a lot of work to get there. It uses the vphantom mentioned by AboAmmar, but it also horizontally centers the to under the lim.
It does it by placing a phantom scripted - to the left of the one-sided limits. But then it must also introduce !!! negative space to compensate.
documentclass{article}
begin{document}
underline{Theorem:} $lim limits_{x to a^{vphantom{-}}} f(x)
Longleftrightarrow !!!lim limits_{^{phantom{-}}x to a^{-}} f(x)
= !!!lim limits_{^{phantom{-}}x to a^{+}} f(x)$
end{document}
answered Dec 18 '18 at 15:37
Steven B. Segletes
152k9193400
answered Dec 18 '18 at 15:37
Steven B. Segletes
152k9193400
answered Dec 18 '18 at 15:37
Steven B. Segletes
152k9193400
answered Dec 18 '18 at 15:37
Steven B. Segletes
152k9193400
152k9193400
add a comment |
add a comment |
If a is a constant, I'd suggest you use uparrow and downarrow to indicate unambiguously that the x is supposed to approach a from below and above, respectively. A very nice side-effect of this notation is that xuparrow a and xdownarrow a take up less space than xto a -- obviating any need to make spacing adjustments.
If, in addition, you wish to assure that xto a and xuparrow a (and xdownarrow a) are typeset at same distance below "lim", just change xto a to xto avphantom{uparrow}.
documentclass{article}
begin{document}
$displaystyle
lim_{xto a} f(x)Longleftrightarrow
lim_{xuparrow a} f(x)=
lim_{xdownarrow a} f(x)$
end{document}
answered Dec 18 '18 at 16:36
Mico
273k30369756
add a comment |
If a is a constant, I'd suggest you use uparrow and downarrow to indicate unambiguously that the x is supposed to approach a from below and above, respectively. A very nice side-effect of this notation is that xuparrow a and xdownarrow a take up less space than xto a -- obviating any need to make spacing adjustments.
If, in addition, you wish to assure that xto a and xuparrow a (and xdownarrow a) are typeset at same distance below "lim", just change xto a to xto avphantom{uparrow}.
documentclass{article}
begin{document}
$displaystyle
lim_{xto a} f(x)Longleftrightarrow
lim_{xuparrow a} f(x)=
lim_{xdownarrow a} f(x)$
end{document}
answered Dec 18 '18 at 16:36
Mico
273k30369756
add a comment |
If a is a constant, I'd suggest you use uparrow and downarrow to indicate unambiguously that the x is supposed to approach a from below and above, respectively. A very nice side-effect of this notation is that xuparrow a and xdownarrow a take up less space than xto a -- obviating any need to make spacing adjustments.
If, in addition, you wish to assure that xto a and xuparrow a (and xdownarrow a) are typeset at same distance below "lim", just change xto a to xto avphantom{uparrow}.
documentclass{article}
begin{document}
$displaystyle
lim_{xto a} f(x)Longleftrightarrow
lim_{xuparrow a} f(x)=
lim_{xdownarrow a} f(x)$
end{document}
answered Dec 18 '18 at 16:36
Mico
273k30369756
If a is a constant, I'd suggest you use uparrow and downarrow to indicate unambiguously that the x is supposed to approach a from below and above, respectively. A very nice side-effect of this notation is that xuparrow a and xdownarrow a take up less space than xto a -- obviating any need to make spacing adjustments.
If, in addition, you wish to assure that xto a and xuparrow a (and xdownarrow a) are typeset at same distance below "lim", just change xto a to xto avphantom{uparrow}.
documentclass{article}
begin{document}
$displaystyle
lim_{xto a} f(x)Longleftrightarrow
lim_{xuparrow a} f(x)=
lim_{xdownarrow a} f(x)$
end{document}
answered Dec 18 '18 at 16:36
Mico
273k30369756
edited Dec 18 '18 at 16:42
answered Dec 18 '18 at 16:36
Mico
273k30369756
answered Dec 18 '18 at 16:36
Mico
273k30369756
answered Dec 18 '18 at 16:36
Mico
273k30369756
273k30369756
add a comment |
add a comment |
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2
You would use a "phantom" glyph, as in
limits_{x to a^{phantom{-}}}to leave extra space in the ordinary limit, but I don't like the look of it at all.– Steven B. Segletes
Dec 18 '18 at 15:31
A bit off-topic, but it seems like you are missing the word "exists".
– Andreas Rejbrand
Dec 18 '18 at 19:52