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Finite, Countable, and Uncountable Sets Video Lecture | CSIR NET Crash Course for Mathematics - CSIR NET Mathematics
FAQs on Finite, Countable, and Uncountable Sets Video Lecture - CSIR NET Crash Course for Mathematics - CSIR NET Mathematics
| 1. What is the difference between finite, countable, and uncountable sets? |  |
Ans. A finite set is a set that has a specific number of elements, while a countable set is a set that can be put in a one-to-one correspondence with the natural numbers. An uncountable set is a set that is not countable, meaning it cannot be put in a one-to-one correspondence with the natural numbers.
| 2. Can you provide an example of a finite set? | |
Ans. Yes, an example of a finite set would be the set of colors in a rainbow, which consists of a specific number of colors - red, orange, yellow, green, blue, indigo, and violet.
| 3. How can we determine if a set is countable or uncountable? | |
Ans. A set is countable if its elements can be listed in a sequence, even if the list is infinite. A set is uncountable if it cannot be put in a one-to-one correspondence with the natural numbers.
| 4. Are real numbers countable or uncountable? | |
Ans. Real numbers are uncountable. This is known as the Cantor's diagonal argument, which proves that the real numbers are uncountable.
| 5. Can a set be both countable and uncountable? | |
Ans. No, a set cannot be both countable and uncountable. A set is either countable or uncountable based on whether it can be put in a one-to-one correspondence with the natural numbers.
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Dec 22, 2024 Last updated |
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