Return to Answer

Assuming that your problem is only for math, then the following is a possible way:

\documentclass{article} \usepackage[T1]{fontenc} \def\displaybrace<{\bgroup\catcode`\>=2 \delcode123="266308 \delcode125="267309 \mathcode123="4266 \mathcode125="5267 \catcode123=12 \catcode125=12 } \begin{document}\pagestyle{empty} \[\displaybrace<{{x},{x,y}}>\] \end{document} 

Any use of a > will close the macro.

If you want to do other things than just display sets, then the following just slight extension is needed:

\documentclass{article} \usepackage[T1]{fontenc} \def\displaybrace<{\bgroup\catcode`\<=1 \catcode`\>=2 \delcode123="266308 \delcode125="267309 \mathcode123="4266 \mathcode125="5267 \catcode123=12 \catcode125=12 } \begin{document}\pagestyle{empty} \[\displaybrace<{{x},{x,y}}>\] \[\omega < \displaybrace<\left{\int_a^b e^<-x^2>\,dx\right}> <z^2 \] \end{document} 

Please note how I used < and > inside \displaybrace. Obviously this makes writing inequalities inside difficult... But we could let + and - play the rôle here played by < and > if you want inequalities inside ... but no additions nor substractions... etc... (using ^^A and ^^B for the \displaybrace argument delimiting could be a possibility, but then it becomes clumsy input inside if one needs groups therein).

And with the above (or the earlier version which did not even yet use < as a substitue for the group opening character) the following is possible:

\[\displaybrace<\Biggl{\biggl{x\biggr},{x,y}\Biggr}>\] 

If one wants to use braces directly also in math mode, the mathcodes and delcodes must be correctly set. This is done here:

\documentclass{article} \usepackage[T1]{fontenc} \def\displaybrace<{\bgroup\catcode`\>=2 \delcode123="266308 \delcode125="267309 \mathcode123="4266 \mathcode125="5267 \catcode123=12 \catcode125=12 } \begin{document}\pagestyle{empty} \[\displaybrace<{{x},{x,y}}>\] \end{document} 

Any use of a > will close the macro. Within the \displaybrace<..stuff...> we have a substitute only for the closing group delimiter with >.

So if one wants to do other things than just display some collection of braces and letters, the following slight extension is needed, which just additionally makes < also serve as opening group character:

\documentclass{article} \usepackage[T1]{fontenc} \def\displaybrace<{\bgroup\catcode`\<=1 \catcode`\>=2 \delcode123="266308 \delcode125="267309 \mathcode123="4266 \mathcode125="5267 \catcode123=12 \catcode125=12 } \begin{document}\pagestyle{empty} \[\displaybrace<{{x},{x,y}}>\] \[\omega < \displaybrace<\left{\int_a^b e^<-x^2>\,dx\right}> <z^2 \] \end{document} 

Please ntake note how I used < and > inside \displaybrace to code the superscript.

More generally any code (be it in text or math mode) where one would have used traditionnally { and } must be written with < and >. And it will work perfectly fine if this constraint is obeyed (except if some macro is used which really requires that { and } are in their traditional habits, or and this is more probable, some macro which would be completely surprised to learn that < and > are now the opening and closing group characters).

Obviously using < and > this way makes writing inequalities impossible... But we could let + and - play the rôle here played by < and >. Again + and - are used for many things so one would have to find something better... 

...for example ^^A and ^^B (which have character codes 1 and 2) could play the rôle here attributed to < and > and this would allow complete freedom to set-up arbitrary math formulas (perhaps your sets are defined mathematically?). But then the input would not be so readable.

Let me explicitely points out that the above code is designed to work well with arbitrary \left or \big.. like constructions.

\[\displaybrace<\Biggl{\biggl{x\biggr},{x,y}\Biggr}>\] 

Assuming that your problem is only for math, then the following is a possible way:

\documentclass{article} \usepackage[T1]{fontenc} \def\displaybrace<{\bgroup\catcode`\>=2 \delcode123="266308 \delcode125="267309 \mathcode123="4266 \mathcode125="5267 \catcode123=12 \catcode125=12 } \begin{document}\pagestyle{empty} \[\displaybrace<{{x},{x,y}}>\] \end{document} 

Any use of a > will close the macro.

If you want to do other things than just display sets, then the following just slight extension is needed:

\documentclass{article} \usepackage[T1]{fontenc} \def\displaybrace<{\bgroup\catcode`\<=1 \catcode`\>=2 \delcode123="266308 \delcode125="267309 \mathcode123="4266 \mathcode125="5267 \catcode123=12 \catcode125=12 } \begin{document}\pagestyle{empty} \[\displaybrace<{{x},{x,y}}>\] \[\omega < \displaybrace<\left{\int_a^b e^<-x^2>\,dx\right}> <z^2 \] \end{document} 

Please note how I used < and > inside \displaybrace. Obviously this makes writing inequalities inside difficult... But we could let + and - play the rôle here played by < and > if you want inequalities inside ... but no additions nor substractions... etc... (using ^^A and ^^B for the \displaybrace argument delimiting could be a possibility, but then it becomes clumsy input inside if one needs groups therein).

Assuming that your problem is only for math, then the following is a possible way:

\documentclass{article} \usepackage[T1]{fontenc} \def\displaybrace<{\bgroup\catcode`\>=2 \delcode123="266308 \delcode125="267309 \mathcode123="4266 \mathcode125="5267 \catcode123=12 \catcode125=12 } \begin{document}\pagestyle{empty} \[\displaybrace<{{x},{x,y}}>\] \end{document} 

Any use of a > will close the macro.

If you want to do other things than just display sets, then the following just slight extension is needed:

\documentclass{article} \usepackage[T1]{fontenc} \def\displaybrace<{\bgroup\catcode`\<=1 \catcode`\>=2 \delcode123="266308 \delcode125="267309 \mathcode123="4266 \mathcode125="5267 \catcode123=12 \catcode125=12 } \begin{document}\pagestyle{empty} \[\displaybrace<{{x},{x,y}}>\] \[\omega < \displaybrace<\left{\int_a^b e^<-x^2>\,dx\right}> <z^2 \] \end{document} 

Please note how I used < and > inside \displaybrace. Obviously this makes writing inequalities inside difficult... But we could let + and - play the rôle here played by < and > if you want inequalities inside ... but no additions nor substractions... etc... (using ^^A and ^^B for the \displaybrace argument delimiting could be a possibility, but then it becomes clumsy input inside if one needs groups therein).

And with the above (or the earlier version which did not even yet use < as a substitue for the group opening character) the following is possible:

\[\displaybrace<\Biggl{\biggl{x\biggr},{x,y}\Biggr}>\] 

Assuming that your problem is only for math, then the following is a possible way:

\documentclass{article} \usepackage[T1]{fontenc} \def\displaybrace<{\bgroup\catcode`\>=2 \delcode123="266308 \delcode125="267309 \mathcode123="4266 \mathcode125="5267 \catcode123=12 \catcode125=12 } \begin{document}\pagestyle{empty} \[\displaybrace<{{x},{x,y}}>\] \end{document} 

Any use of a > will close the macro.

Assuming that your problem is only for math, then the following is a possible way:

\documentclass{article} \usepackage[T1]{fontenc} \def\displaybrace<{\bgroup\catcode`\>=2 \delcode123="266308 \delcode125="267309 \mathcode123="4266 \mathcode125="5267 \catcode123=12 \catcode125=12 } \begin{document}\pagestyle{empty} \[\displaybrace<{{x},{x,y}}>\] \end{document} 

Any use of a > will close the macro.

If you want to do other things than just display sets, then the following just slight extension is needed:

\documentclass{article} \usepackage[T1]{fontenc} \def\displaybrace<{\bgroup\catcode`\<=1 \catcode`\>=2 \delcode123="266308 \delcode125="267309 \mathcode123="4266 \mathcode125="5267 \catcode123=12 \catcode125=12 } \begin{document}\pagestyle{empty} \[\displaybrace<{{x},{x,y}}>\] \[\omega < \displaybrace<\left{\int_a^b e^<-x^2>\,dx\right}> <z^2 \] \end{document} 

Please note how I used < and > inside \displaybrace. Obviously this makes writing inequalities inside difficult... But we could let + and - play the rôle here played by < and > if you want inequalities inside ... but no additions nor substractions... etc... (using ^^A and ^^B for the \displaybrace argument delimiting could be a possibility, but then it becomes clumsy input inside if one needs groups therein).