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Укажите наибольшее целое число, принадлежащее пересечению числовых промежутков. \[ (-\infty ; 5) \text { и }(-8 ; 3) \]

Ask by Hanson Edwards. in Kazakhstan
Nov 01,2024

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Answer

Наибольшее целое число, принадлежащее пересечению числовых промежутков \((- \infty; 5)\) и \((-8; 3)\), это 4.

Solution

Для нахождения наибольшего целого числа, принадлежащего пересечению числовых промежутков \((- \infty; 5)\) и \((-8; 3)\), нужно найти наибольшее целое число, которое удовлетворяет условиям обоих промежутков. Промежуток \((- \infty; 5)\) включает все числа, которые меньше 5, но не включает 5. Промежуток \((-8; 3)\) включает все числа, которые больше -8 и меньше 3, но не включает -8 и 3. Таким образом, наибольшее целое число, которое удовлетворяет условиям обоих промежутков, это 4. Ответ: 4.

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The Deep Dive

Наибольшее целое число, которое принадлежит пересечению промежутков \((-∞; 5)\) и \((-8; 3)\), можно найти, выяснив, какой интервал получится при пересечении. Пересечение данных промежутков будет \((-8; 3)\), так как 3 меньше 5. Наибольшее целое число в этом промежутке — это 2. Таким образом, ответ: 2.

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