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Α α alpha Β β beta Γ γ gamma Δ δ delta Ε ε epsilon
Ζ ζ zeta Η η eta Θ θ theta Ι ι iota Κ κ kappa
Λ λ lambda Ψ ψ psi Μ μ mu Ν ν nu Ξ ξ xi
Ο ο omicron Π π pi Ρ ρ rho Σ σ sigma Τ τ tau
Υ υ upsilon Φ φ phi Χ χ chi Ω ω omega
數學符號表
數學上,有一組常在數學表達式中出現的符號。數學工作者熟悉這些符號,不是每次使用都加以說明。所以,對於數學初學者,下面的列表給出了很多常見的符號包括名稱、讀法和應用領域。另外,第三欄有一個非正式的定義,第四欄有個簡單的例子。
注意,有時候不同符號有相同含義,而有些符號在不同的上下文中有不同的含義。
注意:本條目含有特殊字元。
|符號 |名稱 |定義 |舉例 |
| |讀法 | | |
| |數學領域 | | |
|= |等號 |x = y 表示 x 和 y |1 + 1 = 2 |
| | |是相同的東西或其值相等。 | |
| |等於 | | |
| |所有領域 | | |
|≠ |不等號 |x ≠ y 表示 x 和 y |1 ≠ 2 |
| | |不是相同的的東西或數值。 | |
| |不等於 | | |
| |所有領域 | | |
|< |嚴格不等號 |x < y 表示 x 小於y。 |3 4 |
|> | |x > y 表示 x 大於y。 | |
| |小於,大於 | | |
| |序理論 | | |
|≤ |不等號 |x ≤ y 表示 x 小於等於y。 |3 ≤ 4;5 ≤ 5 |
| | | |5 ≥ 4;5 ≥ 5 |
|≥ | |x ≥ y 表示 x 大於等於y。 | |
| |小於等於,大於等於 | | |
| |序理論 | | |
|+ |加號 |4 + 6 表示 4 加 6。 |2 + 7 = 9 |
| |加 | | |
| |算術 | | |
|− |減號 |9 − 4 表示 9 減 4。 |8 − 3 = 5 |
| |減 | | |
| |算術 | | |
| |負號 |−3 表示 3 的負數。 |−(−5) = 5 |
| |負 | | |
| |算術 | | |
| |補集 |A − B 表示包含所有屬於 A 但不屬於 B |{1,2,4} − {1,3,4} = {2} |
| | |的元素的集合。 | |
| |減 | | |
| |集合論 | | |
|× |乘號 |3 × 4 表示 3 乘以 4。 |7 × 8 = 56 |
| |乘以 | | |
| |算術 | | |
| |直積 |X × Y 表示所有第一個元素屬於 |{1,2} × {3,4} = |
| | |X,第二個元素屬於 Y 的有序對的集合。 |{(1,3),(1,4),(2,3),(2,4)} |
| |… 和…的直積 | | |
| |集合論 | | |
| |叉乘 |u × v 表示向量 u 和 v 的叉乘。 |(1,2,5) × (3,4,−1) = (−22, 16, − 2) |
| |叉乘 | | |
| |向量代數 | | |
|÷ |除號 |6 ÷ 3 或 6 / 3 表示 6 除以 3。 |2 ÷ 4 = 0.5 |
| | | | |
|/ | | |12/4 = 3 |
| |除以 | | |
| |算術 | | |
|√ |根號 |√x 表示其平方為 x 的正數。 |√4 = 2 |
| |…的平方根 | | |
| |實數 | | |
| |復根號 |若用極坐標表示覆數 z = r exp(iφ)(滿足 |√(-1) = i |
| | |-π < φ ≤ π),則 √z = √r exp(iφ/2)。 | |
| |…的平方根 | | |
| |複數 | | |
|| | |絕對值 ||x| 表示實數軸(或復平面)上 x 和 0 ||3| = 3, |-5| = |5| |
| | |的距離。 ||i| = 1, |3+4i| = 5 |
| |…的絕對值 | | |
| |數 | | |
|! |階乘 |n! 表示連乘積 1×2×…×n。 |4! = 1 × 2 × 3 × 4 = 24 |
| |…的階乘 | | |
| |組合論 | | |
|~ |機率分佈 |X ~ D 表示隨機變數 X 機率分佈為 D。 |X ~ N(0,1):標準常態分佈 |
| |滿足分佈 | | |
| |統計學 | | |
|⇒ |實質蘊涵 |A ⇒ B 表示 A 真則 B 也真;A 假則 B 不定 |x = 2 ⇒ x2 = 4 為真,但 x2 = 4 ⇒ x |
| | |。 |= 2 一般情況下為假(因為 x 可以是 −2)。|
|→ | | | |
| | |→ 可能和 ⇒ 一樣, 或者有下面將提到的函數 | |
|⊃ | |的意思。 | |
| | | | |
| | |⊃ 可能和 ⇒ 一樣,或者有下面將提到的父集 | |
| | |的意思。 | |
| |推出,若…則 … | | |
| |命題邏輯 | | |
|⇔ |實質等價 |A ⇔ B 表示 A 真則 B 真,A 假則 B 假。 |x + 5 = y +2 ⇔ x + 3 = y |
| | | | |
|↔ | | | |
| |若且唯若 | | |
| |命題邏輯 | | |
|¬ |邏輯非 |命題 ¬A 為真若且唯若 A 為假。 |¬(¬A) ⇔ A |
| | | |x ≠ y ⇔ ¬(x = y) |
|˜ | |將一條斜線穿過一個符號相當於將 "¬" 放在 | |
| | |該符號前面。 | |
| |非,不 | | |
| |命題邏輯 | | |
|∧ |邏輯與或交運算 |若 A 為真且 B 為真,則命題 A ∧ B 為真; |n < 4 ∧ n >2 ⇔ n = 3,當 n 是自然數 |
| | |否則為假。 | |
| |與 | | |
| |命題邏輯,格理論 | | |
|∨ |邏輯或或並運算 |若 A 或 B(或都)為真,則命題 A ∨ B |n ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3,當 n 是自然數 |
| | |為真;若兩者都假則命題為假。 | |
| |或 | | |
| |命題邏輯,格理論 | | |
| |異或 |若 A 和 B 剛好有一個為真,則命題 A ⊕ B |(¬A) ⊕ A 恆為真,A ⊕ A 恆為假。 |
|⊕ | |為真。 | |
| | | | |
|⊻ | |A ⊻ B 的意義相同。 | |
| |異或 | | |
| |命題邏輯,布爾代數 | | |
|∀ |全稱量詞 |∀ x: P(x) 表示 P(x) 對於所有 x 為真。 |∀ n ∈ N: n2 ≥ n |
| |對所有;對任意;對任一| | |
| |謂詞邏輯 | | |
|∃ |存在量詞 |∃ x: P(x) 表示存在至少一個 x 使得 P(x) |∃ n ∈ N: n 為偶數 |
| | |為真。 | |
| |存在 | | |
| |謂詞邏輯 | | |
|∃! |唯一量詞 |∃! x: P(x) 表示有且僅有一個 x 使得 P(x) |∃! n ∈ N: n + 5 = 2n |
| | |為真。 | |
| |存在唯一 | | |
| |謂詞邏輯 | | |
|:= |定義 |x := y 或 x ≡ y 表示 x 定義為 y的一個名 |cosh x := (1/2)(exp x + exp (−x)) |
| | |字(注意:≡ 也可表示其它意思, | |
|≡ | |例如全等)。 |A XOR B :⇔ (A ∨ B) ∧ ¬(A ∧ B) |
| | | | |
|:⇔ | |P :⇔ Q 表示 P 定義為 Q 的邏輯等價。 | |
| |定義為 | | |
| |所有領域 | | |
|{ , } |集合括弧 |{a,b,c} 表示 a, b,c 組成的集合。 |N = {0,1,2,…} |
| |…的集合 | | |
| |集合論 | | |
|{ : } |集合構造記號 |{x : P(x)} 表示所有滿足 P(x) 的 x |{n ∈ N : n2

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... h(x)= 7-x/3 First we need to compute (f-h)(4) (f*h)(4)=f(4)-h(4), each function can be done separately f(4)=2(4)+5 f(4)=8+5 f(4)=13 H h(4)=(7-4)/3 same process as above h(4)=3/3=h(4)=1 (f-h)(4)=13-1 (f-h)(4)=12 this is the solution after substituting and subtracting The next part we need to replace the x in the f function with the g (f*g)(x)=f(g(x)) (f*g)(x)=f(x2-3) (f*g)(x)=2x2-1 is the result Now we need to do the h function (h*g)(x)=h(g(x)) (h*g)(x)=h(x2-3) (h*g)(x)=7-(x2-3) (h*g)(x)=10-x2 end result The inverse function-- f-1(x)=x-5h-1(x)=-(3-7) By doing problems this way it can save a person and a business a lot of time. A lot of people think they don't need math everyday throughout their life, but in all reality people use math almost everyday in life. The more you know the better off your life will...

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