What ≃ means
Roughly equal, with the exact sense set by the field. The tilde means "similar" and the bar adds "or equal". In physics, engineering and school maths, especially in French-speaking countries, x ≃ 3.14 simply means "about 3.14", the same job as . In analysis, f(x) ≃ g(x) says two functions behave alike as x approaches a limit; some authors mean their ratio tends to 1 (often written ), others only that they stay within constant multiples of each other.
In algebra and topology the sign stops being about numbers. X ≃ Y there usually says two objects are "the same up to" something: isomorphic, or, in topology, homotopy equivalent, meaning one shape can be continuously deformed into the other. A careful author states which meaning they use; if a text doesn't, the subject of the text is your best clue.
Technical notation; clear in context, ambiguous across fields, so define it when writing for mixed readers.
Don't read it as exact equality; it always allows some difference.
Part of the collection
Don't confuse it with
4
Related characters
1
Combination ideas
4Worth knowing
- Leibniz wrote a tilde over a bar for geometric congruence in a 1679 manuscript, an early ancestor of this sign's shape.
Questions people ask
2Is ≃ the same as ?
Often in practice. In physics and engineering many writers use them interchangeably for "approximately equal"; in pure maths ≃ usually carries a stricter, defined meaning.
What does ≃ mean in topology?
Usually homotopy equivalence: two spaces can be deformed into each other continuously. In algebra it often means isomorphic.
More like this
16
How to type or find ≃
- Also called
- simeq · tilde over equals · similar or equal
- Search it as
- asymptotically equal · approximately equal · tilde equal sign · homotopy equivalent · isomorphic · ≃
- Shows up in
- Anything that takes text · its shape is whatever your font draws
≃\2243Codes and encoding1 code points
A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.