物理学/数学中常用的“等号”

=

=

=:相等(equality) (拓扑)同构(isomorphic)

\sim

∼:渐近等于( asymptotically equal)

\approx

≈: (数学)约等于(别的形式:

=

\sim=

∼=,

\fallingdotseq

≒)(Almost equal to); (拓扑)同胚(Homeomorphic to)

\cong

≅: (数学)大约等于(Approximately equal to); (几何)一致,全等(Congruent to); (代数、范畴论、逻辑)同构到(Isomorphic to)

\backsim

∽:(几何)相似符号(similar)

\equiv

≡:(数学)相当于(is equivalent to); (数学)等于(identically equal to),函数

f

f

f和

g

g

g满足

f

g

f\equiv g

f≡g,当且仅当它们各自的定义域重合,且对于这个定义域中的所有

x

x

x,

f

(

x

)

=

g

(

x

)

f(x)=g(x)

f(x)=g(x); (数学)被定义为,被设置为(is defined as, is set to); (数论)一致(is congruent to);用于模的计算(used in calculations of modulo),如

15

3

m

o

d

4

15\equiv 3\ \mathrm{mod}\ 4

15≡3 mod 4,因为15和3除以4余数都是3; (逻辑,日期(dated))(逻辑,日期)当且仅当(if and only if); (逻辑)初等等价(elementary equivalence)

\propto

∝:正比例符号(is proportional to)

\ncong

≆: (数学)既不近似也不等于(Neither approximately nor actually equal to); (几何学)不一致的(Not congruent to); (数学)不同构的(Not isomorphic to)

\simeq

≃: 渐近等于(Asymptotically equal to); 大约等于(Approximately equal to); 同伦等价(homotopy equivalence)

~

\tilde{\neq}

=~​:大约但不等于(Approximately but not actually equal to)

\neq

=:不等于

\cancel{\simeq}

​:不渐近等于(Not asymptotically equal to)

=

d

e

f

\overset{\mathbf{def}}{=}

=def:根据定义等于(Equal to by definition)

\triangleq

≜:表示"是定义为"或"等于"的含义。