COUNTABLY Meaning and
Definition
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Countably is an adverb that is used in mathematics to describe a set that can be put into a one-to-one correspondence with the natural numbers, which are the positive integers starting from one (1, 2, 3, 4, 5, ...). In other words, a countable set is a set that can be listed in a specific order in such a way that every element can be paired with a unique natural number.
When a set is countable, it means that it has a finite number of elements, or an infinite number of elements that can be arranged in a list. However, it is important to note that countable does not imply that the set is small or easily comprehensible. For example, the set of all positive even numbers (2, 4, 6, 8, ...) is countable because it can be listed and paired with the natural numbers, even though the set itself is infinite.
Countability is a fundamental concept in mathematics and has various applications across different branches, such as calculus, set theory, and number theory. It allows mathematicians to study and analyze the properties and behavior of infinite sets in a systematic and rigorous manner. The ability to classify sets as countable or uncountable is crucial in many areas of mathematical reasoning and helps provide a foundation for further exploration and discovery.
Common Misspellings for COUNTABLY
Etymology of COUNTABLY
The word "countably" is derived from the verb "count", which can be traced back to the Old French word "compter" meaning "to count" or "reckon", ultimately derived from the Latin word "computare" meaning "to calculate". The suffix "-ably" is added to "count" to form "countably", indicating that something can be counted or enumerated.
