{ "definitions": { "F": [ "set", {} ], "x": [ { "Q12916": "real number (quantity along a continuous line)" } ], "y": [ { "Q12916": "real number (quantity along a continuous line)" } ], "\\mathcal{R}": [ { "Q12916": "real number (quantity along a continuous line)" } ], "b": [ { "Q12503": "integer (number that can be written without a fractional or decimal component)" } ], "n": [ { "Q12503": "integer (number that can be written without a fractional or decimal component)" } ] }, "constraints": [], "math_inputtex": " F = \\{ (x,y) : x \\in \\mathcal{R}^b,\\, y \\in \\mathcal{R}^n,\\; x=y \\}.", "math_inputtex_semantic": "\\w{Q36161}{F} = \\{ (\\w{Q12916}{x},\\w{Q12916}{y}) : x \\in {\\mathcal{R}^{\\w{Q12503}{b}},\\, y \\in \\mathcal{R}^{\\w{Q12503}{n}},\\; x=y \\}", "correct_tex": "F = \\{ (x,y) : x \\in \\mathcal{R}^b,\\, y \\in \\mathcal{R}^n,\\; x=y \\}", "correct_mml": "\n \n \n F\n =\n \n {\n \n (\n x\n ,\n y\n )\n \n :\n \n \n x\n ∈\n \n ℛ\n b\n \n \n ,\n \n \n y\n ∈\n \n ℛ\n n\n \n \n ,\n \n x\n =\n y\n \n \n \n }\n \n \n \n \n \n Q36161\n \n conditional-set\n \n Q12916\n Q12916\n \n \n formulae-sequence\n \n \n Q12916\n \n \n ℛ\n Q12503\n \n \n \n formulae-sequence\n \n \n Q12916\n \n \n ℛ\n Q12503\n \n \n \n \n Q12916\n Q12916\n \n \n \n \n \n \n F=\\{(x,y):x\\in{\\mathcal{R}^{b},\\,y\\in\\mathcal{R}^{n},\\;x=y\\}\\)\\@add@PDF@RDFa@triples\\end{document}}\n \n", "uri": "https://en.formulasearchengine.com/w/index.php?oldid=28184#math28184.6", "title": "Projections_onto_convex_sets", "type": "definition", "check": { "tree": false } }