non-equipotent sets
[/nɑːn ˌɛkwɪˈpoʊtənt sɛts/]
nounpl: non-equipotent sets
conjuntos não equipotentes
1. In mathematics, sets that do not have the same cardinality; sets between which no one-to-one correspondence (bijection) can be established
The set of natural numbers and the set of real numbers are non-equipotent sets because there is no bijection between them.
O conjunto dos números naturais e o conjunto dos números reais são conjuntos não equipotentes porque não existe uma bijeção entre eles.
2. Sets that cannot be put into one-to-one correspondence with each other, indicating different sizes in the context of infinite sets
Non-equipotent sets demonstrate that some infinities are larger than others, as proven by Cantor's diagonal argument.
Conjuntos não equipotentes demonstram que alguns infinitos são maiores que outros, conforme provado pelo argumento diagonal de Cantor.
This is a formal mathematical term used exclusively in academic contexts, particularly in set theory, topology, and advanced mathematics courses. It reflects Cantor's revolutionary work on infinity and is fundamental to modern mathematical analysis. The concept is taught identically in Portuguese-speaking countries and English-speaking countries, making it a truly universal mathematical term.
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