Замечание. Для любого
![](data:image/png;base64,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)
, если множество
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADpSURBVDjLY2hsbGSgBDPQ3QAgYCTbgOosFyNjt7wUsgwoL0/jdZNh2Gsc3eBDsgEgZ0cZMywE0v/JMqA+0tjX2M2tVpZB9qZHXr0hSQaA/C1rHN3TEG3sw8BgfDe2vl6SaAPA/jZ2qwtNS+OrjTT0I8kAkL+jjRkWAOm/IMzIwPCPQcZjT1pHBw9RBoD9HdvgDeODA5EYA0A2w/yNLA42wDhqId6UCARMYL/KuO1NKy/nhRmYlhbKB0oDsm45JQwMq5iwGlBfHytpzMBwG+ZnWY+8IpB4Q6yxN0wMjGXddyF7g2Ho5UZ0DABRWIG2vnPnxwAAAABJRU5ErkJggg==)
, определяющее отношение эквивалентности, содержит полосу
![](data:image/png;base64,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)
, то оно совпадает со всей плоскостью. В самом деле, вместе с любой точкой
![](data:image/png;base64,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)
множество
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADpSURBVDjLY2hsbGSgBDPQ3QAgYCTbgOosFyNjt7wUsgwoL0/jdZNh2Gsc3eBDsgEgZ0cZMywE0v/JMqA+0tjX2M2tVpZB9qZHXr0hSQaA/C1rHN3TEG3sw8BgfDe2vl6SaAPA/jZ2qwtNS+OrjTT0I8kAkL+jjRkWAOm/IMzIwPCPQcZjT1pHBw9RBoD9HdvgDeODA5EYA0A2w/yNLA42wDhqId6UCARMYL/KuO1NKy/nhRmYlhbKB0oDsm45JQwMq5iwGlBfHytpzMBwG+ZnWY+8IpB4Q6yxN0wMjGXddyF7g2Ho5UZ0DABRWIG2vnPnxwAAAABJRU5ErkJggg==)
содержит все внутренние точки квадрата с вершинами
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
, т.е. полосу
![](data:image/png;base64,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)
. Ясно, что таким образом свойство "принадлежать
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADrSURBVDjLY2hsbGSgBDPQ3QAgYCTbgOosFyNjt7wUsgwoTwvlc5Nh2Gsc3eBDsgEgZ0cZMywE0v9JNgCkuT7S2NfYza1WlkH2pkdevSFJBoD8LWsc3dMQbezDwGB8N7a+XpJoA8D+NnarC01L46uNNPQjyQCQ06ONGRYA6b8gzMjA8I9BxmNPWkcHD0ED4P6ObfCGiYEDkRgDQJph/kYWBxtgHL0Ab0oEAiawX2Xc9qaVl/PCDEyDpgFZt6wSBoZVTFgNqK+PlTRmYLgN9fMfWY+sIpB4Q6yxNywcQOIMsu67kL3BMPRyIzoGAAq4fmgf1ilPAAAAAElFTkSuQmCC)
" распространяется на все точки плоскости.
2 Пример. (периодичность). Возьмем которое число. Пусть множество
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADrSURBVDjLY2hsbGSgBDPQ3QAgYCTbgOosFyNjt7wUsgwoTwvlc5Nh2Gsc3eBDsgEgZ0cZMywE0v9JNgCkuT7S2NfYza1WlkH2pkdevSFJBoD8LWsc3dMQbezDwGB8N7a+XpJoA8D+NnarC01L46uNNPQjyQCQ06ONGRYA6b8gzMjA8I9BxmNPWkcHD0ED4P6ObfCGiYEDkRgDQJph/kYWBxtgHL0Ab0oEAiawX2Xc9qaVl/PCDEyDpgFZt6wSBoZVTFgNqK+PlTRmYLgN9fMfWY+sIpB4Q6yxNywcQOIMsu67kL3BMPRyIzoGAAq4fmgf1ilPAAAAAElFTkSuQmCC)
состоит из прямых
![](data:image/png;base64,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)
, где
![](data:image/png;base64,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)
– произвольное целое число. Выполнение свойств
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
очевидно, и если
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
, то
![](data:image/png;base64,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)
.
3 Пример. "Все константы равны единице, кроме нуля". (Такое утверждение высказал И.М. Гельфанд на одной из своих лекций.) В этом примере множество
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADrSURBVDjLY2hsbGSgBDPQ3QAgYCTbgOosFyNjt7wUsgwoTwvlc5Nh2Gsc3eBDsgEgZ0cZMywE0v9JNgCkuT7S2NfYza1WlkH2pkdevSFJBoD8LWsc3dMQbezDwGB8N7a+XpJoA8D+NnarC01L46uNNPQjyQCQ06ONGRYA6b8gzMjA8I9BxmNPWkcHD0ED4P6ObfCGiYEDkRgDQJph/kYWBxtgHL0Ab0oEAiawX2Xc9qaVl/PCDEyDpgFZt6wSBoZVTFgNqK+PlTRmYLgN9fMfWY+sIpB4Q6yxNywcQOIMsu67kL3BMPRyIzoGAAq4fmgf1ilPAAAAAElFTkSuQmCC)
есть вся плоскость с выброшенными осями координат и добавленным началом координат. Иначе говоря,
![](data:image/png;base64,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)
всегда, кроме случая
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
и ему симметричного. Если точки
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADcAAAATCAYAAAA05pVmAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAIGSURBVFjD7VcxTsMwFP1kLuwUzB2oy8xSBaOWMQiIMoE8VFUGGDwglHTLwgGYCiyIHqHlIqjiAi1XQMLfqWkoiZsgpLaokayo1rf93n/v/7jQbrfhv45/Syw3OfmsAXSteQLtAliI48/IjTe0glN6BPSsM09yZxQ69DQ4AoUpX6KNpFwK9/L9YSIWqxrH/5wzg9DnJONMLkGCMR73Ps/+00Atzp0NRqCPm1AvrM/KTujRujoQyKjWvK4gOKU0zpGDHo+ikkkNFbfNXnSc2o+wvmnd15kyzuF8I5nYVHJCeGUK8IYgmR/sFrWNz8glVE4eWza5KmLh0KUNAPrmBcEm/o4iXrKpfWMip0fgs10CMFLrhShnklPgCkiecdA7sVtXxdeRV51QTDJjvpOzwVgqmRI3Yf7lzJrLK/n0EIKvs214waIvRC7wNtEx1A0bKsm2faxVzKjxb/0gjdTMbjlWYiglHzhCbJmUxDrzbXpRrZInackHPVeInEzKdbNW2WP+eZZSQjhbMnaQtx/kPXyQVke6K2IDwQyqhBD2jIojWW216W6aHFhjqDhh7La6w+6yai1uPnRgUvVPbyiTOo2JI9ADAr2kXZIOSAOmyKnuXAz4wly/YnXZfrILayXRbq7rHi7l3TLN1mP7drngZVQtT/0szcV5YlUy/M03dfWvYEVuRW4xxyeHh8xfqk2uzwAAAABJRU5ErkJggg==)
,
![](data:image/png;base64,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)
принадлежат
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADpSURBVDjLY2hsbGSgBDPQ3QAgYCTbgOosFyNjt7wUsgwoL0/jdZNh2Gsc3eBDsgEgZ0cZMywE0v/JMqA+0tjX2M2tVpZB9qZHXr0hSQaA/C1rHN3TEG3sw8BgfDe2vl6SaAPA/jZ2qwtNS+OrjTT0I8kAkL+jjRkWAOm/IMzIwPCPQcZjT1pHBw9RBoD9HdvgDeODA5EYA0A2w/yNLA42wDhqId6UCARMYL/KuO1NKy/nhRmYlhbKB0oDsm45JQwMq5iwGlBfHytpzMBwG+ZnWY+8IpB4Q6yxN0wMjGXddyF7g2Ho5UZ0DABRWIG2vnPnxwAAAABJRU5ErkJggg==)
, то либо
![](data:image/png;base64,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)
, и тогда
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACcAAAAVCAYAAADFEfeTAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAF6SURBVEjH7ZZNSsNAFMdfuy7u+zGewTr2BhKetC4jtCErYRZBslAhC5FJdtl4AFfd5wrtRUR7geIRFMyMTczHJAQbScAGHiHDzOT35v9/LwHP86Ct0VqwRuHCqxNGdxed1sAJGEsj9+H9UwSd80sVYCNwfE5DGPpqct7n3OxTgDcB2Dic77MejmBNDXcWjbkGncEI18z3e6VwQeyDoJv2x89zfm5R5NdwG8cEyAvafFw2poRbUFhKLyQycU06BYKrbGbxXHV8AF0ss/vLUwK6EZLGcN/SbpKnWShrdgMhhUa1xyzcb2JvuOwxO445QLT1OmRVwsn3wXs1uEQmwm+2pl0lN9tHVpW/Hqzz00qeS8GF5S0WTtC+rrVaCaySreNG9DyFp0vLnSA+nR3jcx1eS0m7KzCdsSPH0Yeyz5nutFKfi7KLGuVf9DsLyW0kvwosBydMHBndMIyL1nz4pVEJBsxhA+mJgmyagwPYApAt3rknh/+5A9x/hPsCDrOJuc9hWBcAAAAASUVORK5CYII=)
,
![](data:image/png;base64,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)
, либо
![](data:image/png;base64,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)
, и тогда
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
. В обоих случаях
![](data:image/png;base64,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)
.
4 Пример. (Все целые числа равны друг другу.) Множество
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADrSURBVDjLY2hsbGSgBDPQ3QAgYCTbgOosFyNjt7wUsgwoTwvlc5Nh2Gsc3eBDsgEgZ0cZMywE0v9JNgCkuT7S2NfYza1WlkH2pkdevSFJBoD8LWsc3dMQbezDwGB8N7a+XpJoA8D+NnarC01L46uNNPQjyQCQ06ONGRYA6b8gzMjA8I9BxmNPWkcHD0ED4P6ObfCGiYEDkRgDQJph/kYWBxtgHL0Ab0oEAiawX2Xc9qaVl/PCDEyDpgFZt6wSBoZVTFgNqK+PlTRmYLgN9fMfWY+sIpB4Q6yxNywcQOIMsu67kL3BMPRyIzoGAAq4fmgf1ilPAAAAAElFTkSuQmCC)
состоит из главной диагонали и всех точек с целыми координатами.
Очевидно, можно рассматривать и конечные варианты такой эквивалентности типа
![](data:image/png;base64,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)
5 Пример. (Все числа, не большие единицы по модулю, равны друг другу.) Множество
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADpSURBVDjLY2hsbGSgBDPQ3QAgYCTbgOosFyNjt7wUsgwoL0/jdZNh2Gsc3eBDsgEgZ0cZMywE0v/JMqA+0tjX2M2tVpZB9qZHXr0hSQaA/C1rHN3TEG3sw8BgfDe2vl6SaAPA/jZ2qwtNS+OrjTT0I8kAkL+jjRkWAOm/IMzIwPCPQcZjT1pHBw9RBoD9HdvgDeODA5EYA0A2w/yNLA42wDhqId6UCARMYL/KuO1NKy/nhRmYlhbKB0oDsm45JQwMq5iwGlBfHytpzMBwG+ZnWY+8IpB4Q6yxN0wMjGXddyF7g2Ho5UZ0DABRWIG2vnPnxwAAAABJRU5ErkJggg==)
состоит из диагонали и замкнутого единичного квадрата. Очевидно, множество, состоящее из открытого (или полузамкнутого:
![](data:image/png;base64,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)
) квадрата, также дает эквивалентность.
2. Отношение толерантности
2.1 Определения, примеры, свойства
2.1.1 Определение
Отношение
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADpSURBVDjLY2hsbGSgBDPQ3QAgYCTbgOosFyNjt7wUsgwoL0/jdZNh2Gsc3eBDsgEgZ0cZMywE0v/JMqA+0tjX2M2tVpZB9qZHXr0hSQaA/C1rHN3TEG3sw8BgfDe2vl6SaAPA/jZ2qwtNS+OrjTT0I8kAkL+jjRkWAOm/IMzIwPCPQcZjT1pHBw9RBoD9HdvgDeODA5EYA0A2w/yNLA42wDhqId6UCARMYL/KuO1NKy/nhRmYlhbKB0oDsm45JQwMq5iwGlBfHytpzMBwG+ZnWY+8IpB4Q6yxN0wMjGXddyF7g2Ho5UZ0DABRWIG2vnPnxwAAAABJRU5ErkJggg==)
на множестве
![](data:image/png;base64,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)
называется
толерантностью или
отношением толерантности, если оно рефлексивно и симметрично.
Пример. Множество
![](data:image/png;base64,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)
состоит из четырехбуквенных русских слов – нарицательных существительных в именительном падеже. Будем называть такие слова сходными, если они отличаются не более чем на одну букву. Известная задача "Превращение мухи в слона" в точных терминах формулируется так:
Найти такую последовательность слов, начинающуюся словом "муха" и кончающуюся словом "слон", любые два соседних слова в которой сходны (в смысле только что данного определения).
Приведем решение этой задачи: Муха – мура – тура – тара – кара – каре – кафе – кафр – каюр – каюк – крюк – крок – срок – сток – стон – слон.
2.1.2 Пример
Пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADxSURBVDjLY2hsbGSgBDPQxAAgYIJixlUINhNRBtTneRjKMjC8Amr4ZxxZ7xttzLAAyP7LyGB8N7a8XIooF9TXx0oaMciekpNjuG4c2+Dd0ZHG4yHDsEfWLaeYOAMijX0ZZI1PRubVq4L4cAM88oqIMiDKmGGhcXSDD4xfneViJMcgd8Mjr96QcBiAnW+0O7a+XhLEBwVihBHDIgbj6AVEBSLINllZj1WhaWl8oJCPNGZayMBgfBtmIEEDctxkS0ChDsfGUfOJTgfgwJKVXYnNrwQNAPkV6HxjmPNJNgAY8vPhzpZ135XW0cEzcHlhaBkAAHQ7gLaXyiXAAAAAAElFTkSuQmCC)
– натуральное число. Обозначим через
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAZCAYAAAAxFw7TAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAFnSURBVEjH7ZU9UsJAFMf/UCM9Q5bOA5DHEZywjmAXx5ChsdjCYVJIkcKRTbpcgUq05AjICbwCnAC9go7ZnfAZC5LQafFmJzv7fvM+/u8FYRjilIZ/4MamQBlbK+nHyZkZ6PvirG2U5jHgSxk5suv7dt2yvJtcwB7hBeRO1t8uYRKDv8kNOpmBUvZrJtj7xf2jub6LIlHhjda4L2UtM1A7M7zBvH0FpuVNlJzfiSiq5Eo56NOVrt8BtFCXpcebDFjBaM9tIaq5gEoWu9JIoB8w+PyYdFPAwKXOYScHFhsC7JN7spkZqJyV5vZSd6gL0PKYDqeAWn+ghe37dTUhQthVLXDqPacckwnanaQ9oNIfkTvSJ7BYT8lvsOTNkixrpBrHrMGw8HLQ2bDLmSed8zgQWQioImw1+Fh1XtWYce+hGDCGNJ2na7UwCDTbbVj+dHWN2epQTplhKirT7AUn2dhbBaQj+8M/qR9r4MoXREo5HwAAAABJRU5ErkJggg==)
– совокупность всех непустых подмножеств множества
![](data:image/png;base64,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)
. Два таких подмножества объявим толерантными, если у них есть хотя бы один общий элемент. Законность такого определения очевидна: рефлексивность и симметричность отношения легко проверяются.
Множество
![](data:image/png;base64,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)
называется
![](data:image/png;base64,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)
-мерным симплексом. Это понятие обобщает понятия отрезка, треугольника и тетраэдра на многомерный случай. Числа
![](data:image/png;base64,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)
интерпретируются как вершины симплекса. Двухэлементные подмножества – как ребра, трехэлементные как плоские грани,
![](data:image/png;base64,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)
-элементные подмножества – как
![](data:image/png;base64,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)
-мерные грани. Толерантность граней симплекса
![](data:image/png;base64,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)
означает их геометрическую инцидентность – наличие общих вершин. Число всех элементов из
![](data:image/png;base64,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)
равно
![](data:image/png;base64,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)
.
Множество
![](data:image/png;base64,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)
с заданным на нем отношением толерантности
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACkSURBVDjLY2hsbGQgFTNQRRMQMAIxExpmxKkJJFkfaewLpP8C8T8o/ZdB1nNXWkcHD1ZNDdHGPgzG0Qs6OtJ4PGRlV3rk1RsSdF5WVpYKiK7OcjGSlfVcgWw6wYCIMmZYaBzd4EN0QNTXx0oaMRjtjq2vlyReEyggjKMWwgKGKE0gp8m65ZSUl4dKGxtH1xGlKc9DtggS1Ma3cTmRYeCSEc00AQD3WxLL0fFucAAAAABJRU5ErkJggg==)
называется
пространством толерантности. Таким образом, пространство толерантности есть пара
![](data:image/png;base64,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)
.
2.1.3 Пример
Пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADvSURBVDjLY2hsbGSgFmaguWGrGBiYGFAxIz5xvIZFGTPMByr8B8T/gfivrEdeET5xgt7McZMtZmCQfe2RV29IjDhew6KMGBYxGEcvIFYcp2H19bGSxgwMd42jG3yIEcdvWKSxLwOD8d3Q8nJp5ACvjTT0A4rfia2vlyTaMGBAL4QG9F80/B+XF7Ea1tGRxuMhw7AHPaYIeRGrYdVZLkayDLI30WOrIdrYBxiLb7DFIk7DgFFfwiDrsTuto4OHGHGshoFSc3l5qDTIK7JuOSUMDKuYsIujpnqshuV5yBahBLZx1Hxs4uhhSd+MPigMAwAOCbjv7P8bIwAAAABJRU5ErkJggg==)
– произвольное множество. Обозначим через
![](data:image/png;base64,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)
совокупность всех непустых подмножеств множества
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADcSURBVDjLzZNBCoMwEEWney+gmEPI3EGysAeowa0ryUKFLKO7HEPv4UW68AY9Q23UjZWYptCWBobAIzz4MxNo2xY+VfB1mT6nfdm4VcYQOv3wrmuab0J5aeMvYxYxqQDIjXIZuXCrLEXoAdPelR/KpMx8BBiRNYkLt8oahgkAjpkQwbbZ8oLnhUvpO8uWKGuj9zUdRTTKlMo9GsJA4qJ6J6JRJjmNCJDrflprdPMUD2V69DWEdMiV8ly4UTY3WIgsmKPoiPV2603cKuOUlE/NRtaZ+H7rf/vR/0L2AJw1txyixfYGAAAAAElFTkSuQmCC)
. Толерантность
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACmSURBVDjLY2hsbGQgFTNQRRMQMAIxEypexYRTE0hDfaSxL5D+C8T/oPQfBln3XWkdHTxYNTVEG/swGEfN7+hI4/GQlV3pkVdvSNB5WVlZKiC6OsvFSFbWcwWy6QQDIsqYYaFxbIM30QFRXh4rZcRgtDu2vl6SaE3ggDCOXgALGKI0gZwm65ZTUl4eKm1sHF1HlKYsD9kicDAzGN/G5USGgUtGNNMEAINeE15eX9FhAAAAAElFTkSuQmCC)
на
![](data:image/png;base64,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)
задается условием:
![](data:image/png;base64,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)
, если
![](data:image/png;base64,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)
.
Пространство
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAXCAYAAADgKtSgAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAF0SURBVEjH7ZU9bsIwFMdfOgM7AnfrAci7AkotAWMqhShLBw8IZWgHD0h1suUMnWi39grkBFyB9gK0V+hHXj5oCGEA06mN9BTZin62//o9B8IwhN8q+IcfBE8eI6mzvIxiThsupWjyLsQJ7IMKHTWS0u5Yln+lDR8jPAC682LsIsyTRT7RDYZacKW8tgls2Z/MzGIuikTj8hzvPaXaWnACcQYLMMeP5Yxdzq9FFDW0Ywk8HKR5VxY4mS3K5z0G8AZdHgspm9rwXD+jdoEDI9mBBy4Oq0ZMLXYLwN65r3p1PVAZG3vhBCKnt+JxcASAr2VTfM5uSM1k/sVR/kUqAMAXML4on3DXb8CVLWWHdiKE3UqbqeT8j1HsqThNFp+5rKq65Teie5e+AVZFd1bBGxjjz7YQLdpEerqa745SLIuKYsk3sKd7j4JTfAWsGpEWnC4wE8yY8iU7ZpM+UkR1qh4WR+b9Or0pvWCw6WRg65Ps/G/85r4BnknpgOUVzr8AAAAASUVORK5CYII=)
играет роль "универсального" пространства толерантности.
2.1.4 Пример
Возьмем произвольное множество
![](data:image/png;base64,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)
(для наглядности можно представить отрезок на прямой). Пространство толерантности
![](data:image/png;base64,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)
состоит из всех числовых функций, определенных на этом множестве, т.е. функций, которые каждому элементу из
![](data:image/png;base64,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)
сопоставляют некоторое число. Две функции будут толерантными, если хотя бы на одном элементе из
![](data:image/png;base64,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)
эти функции принимают одно и тоже значение (если, другими словами, графики этих функций пересекаются).
Существует еще один способ задания отношений толерантности. Рассмотрим соответствие
![](data:image/png;base64,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)
. Множество всех образов элемента
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACzSURBVDjLY2hsbGQgFTMMjCYgYARiJhDGIsaIVVNDrLE3UPIvA4Psa5esaiOQwvpIY1+wmKznrrSODh6czstxky1mMIpaBKaNoxcQ5af6PA9DWQaGN7JuOcVEB0R5eRqvhwzDHuPIel+iNIH8kedmnGJiIrucwThqIUwMqyZYKIE8LuuRVwR2oqzHytC0ND6QIR559YYYmvI8ZIvAoQT1eEdHGo+HLMNukBjIkEGQImiqCQDUXgyBpkSnawAAAABJRU5ErkJggg==)
при соответствии
![](data:image/png;base64,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)
мы обозначим
![](data:image/png;base64,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)
. Отношение
![](data:image/png;base64,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)
на множестве
![](data:image/png;base64,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)
задается условием:
![](data:image/png;base64,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)
, если у элементов
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADCSURBVDjLY2hsbGQgFTMMjKb/DAyMDAwMzFDMiCoWyoxVU32ssTdQwR9GBtlXLlnVxqsYGJiqI019QWIMsh470zo6eHA6L89DtojBKGJRjptsMYNx1Hyi/NRQ7GEgy8DwWtYjr4jogOgoT+P1kGHYYxxZ70uUJpDH89yMU0xMZJcBnbYQKTAYMTSBPA0KJZDHZT1yCsFOlHVfGZqWxg8yxKO4wQBDU46HbCE4lKAe7+hI4/GQZdgJEgMZMghSBE01AQDitQ8zvoWhcgAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADrSURBVDjL1ZI/DgFBGMUfWhcgZs+A4QayPkFJwmQqyRaKaRRbiMxst41ep98j4CIkDuAQEkZCxN+JiEQxxZt8v+S9732IogifPnwVToA0gAyQpC9DQOpaP4X7HPPj8B4FWgVxnLV/RvImGC3P+qVtI3gL4Fupdc7qOA6yPvcnTrBWVGJga1K6ZHUYyjyR6jgtTGuZ48CWC9OyeZXvd88u3OGebo+HtXKV1MC5KpuRClgxomnFo9lt1vcwwxIobx7ZvYOvu7RdCyEazkdy2jCrJ0EY5BsMCy5N0xk2Iyp6wA7wdjQyxd/f9n/AB8j8bUTpDv6cAAAAAElFTkSuQmCC)
существует образ, т.е. если
![](data:image/png;base64,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)
.