How Do You Spell BIJECTION?

Pronunciation: [ba͡ɪd͡ʒˈɛkʃən] (IPA)

"Bijection" is a mathematical term that refers to a one-to-one correspondence between two sets. The spelling of this word can be explained using IPA phonetic transcription: /baɪ̯ˈdʒɛk.ʃən/. The first syllable "bi" rhymes with "eye" and the second syllable "jec" is pronounced like "check". The final syllable "tion" is pronounced as "shun". With this knowledge of IPA transcription, it becomes easier to recognize and spell this term correctly in mathematical contexts.

BIJECTION Meaning and Definition

1. A bijection, also known as a one-to-one correspondence, is a term from mathematics that describes a specific type of function between two sets. In mathematics, a function is a rule that assigns each element from one set, called the domain, to a unique element in another set, called the codomain. A bijection is a function that exhibits both injectivity and surjectivity, meaning that it is both one-to-one and onto.

   Injectivity refers to the property of a function where distinct elements from the domain are mapped to distinct elements in the codomain. In other words, each element in the domain has a unique element associated with it in the codomain.

   Surjectivity, on the other hand, means that every element in the codomain has at least one element in the domain that maps to it. This implies that every element in the codomain is reached by the function.

   The combination of both injectivity and surjectivity in a function ensures that every element in the domain is paired with a distinct element in the codomain, and vice versa, establishing a one-to-one correspondence between the two sets. This one-to-one correspondence is what characterizes a bijection.

   Bijections are often used in various areas of mathematics where it is important to establish that two sets have the same cardinality or size. In this context, a bijection serves as a bridge between the sets, ensuring a reliable and accurate comparison between their elements.

Common Misspellings for BIJECTION

• 0bjection
• Ritection

Etymology of BIJECTION

The word "bijection" in mathematics is derived from the French term "bijection". It comes from the combination of two French words: "bi-" meaning "two" or "twice", and "jection" derived from the word "injection", which means "injection" or "mapping". Thus, "bijection" refers to a function or mapping between two sets that is both injective (one-to-one) and surjective (onto), meaning that each element of one set corresponds to exactly one element of the other set. The term was first used in mathematics in the early 20th century.

Plural form of BIJECTION is BIJECTIONS