Greater Than、Less Than、At Least、No More Than:不等式英文

有個學生喺一份備試練習卷上做緊一條應用題:「Find the values of x such that x ≥ 5。」佢將個符號讀做「x bigger than five」,然後圈晒所有大過五嘅數字,但跳過咗五本身。蝕咗兩分 —— 唔係因為佢做錯數學,而係因為佢睇漏咗 greater-than 符號下面嗰條細線。Greater than 同 greater than or equal to 係唔同嘅關係,而英文用一兩個額外嘅字將呢個分別講清楚。同一個陷阱亦都出現喺日常生活:一塊牌寫住「no more than five items per customer」,啲顧客就諗緊五件係咪得。

點解呢樣嘢重要

不等式出現喺測驗分數、年齡限制、交通標誌、鋪頭規則、合約、食譜同軟件入面。「Children under 12 ride free。」「You must be at least 18 to apply。」「Use no more than 200 grams of sugar。」每個短語都決定一個特定數字係入定出。讀錯個字,你就會犯規、錯失機會,或者喺寫作題目蝕分。好消息係成個系統都係圍住五六個細細個短語建立。

規律

四個核心符號係 >、<、≥ 同 ≤,而每一個都有一個口語英文形式。

> 係 greater than。所以 x > 5 讀做「x is greater than five」—— x 高過 五但 唔等於 五。

< 係 less than。所以 x < 5 讀做「x is less than five」—— x 低過五,唔等於佢。

≥ 係 greater than or equal to。嗰條細線即係 or equal。所以 x ≥ 5 讀做「x is greater than or equal to five」。喺日常英文,呢個亦都用 at least 呢個短語嚟表達:「at least five」即係 5 或更多。

≤ 係 less than or equal to。日常英文講 at most、no more than 或者 up to:「at most five」同「no more than five」都係解 5 或更少。

仲有兩個有用嘅符號:

≠ 係 not equal to。所以 x ≠ 0 讀做「x is not equal to zero」或者「x does not equal zero」。

≈ 係 approximately equal to。讀做「approximately equal to」,或者喺口語入面讀「about」或者「roughly equal to」。

四個對日常英文有用嘅不等式短語:

• More than = 嚴格高過。More than five people came —— 六個或更多。
• Less than 或者 fewer than = 嚴格低過。(可數嘅嘢用 fewer than:fewer than five people;不可數嘅量或者配數字用 less than:less than five dollars。)
• At least = ≥。At least five 包括 5。
• At most / no more than / up to = ≤。No more than five 包括 5。

關於 above 同 below 嘅一句:喺數字語境,above five 即係嚴格大過五,而 below five 即係嚴格細過五。邊界數字本身被排除。

錯誤 / 自然 / 點解

常見情境

讀一條測驗題。「Find all integers x such that 2 ≤ x ≤ 8。」自然讀法係「x is between two and eight, inclusive」或者「x is greater than or equal to two and less than or equal to eight」。Inclusive 呢個字係日常英文講 兩個端點都計 嘅方法。

招聘廣告。「Applicants must have at least three years of experience。」即係 3 年或更多。如果你啱啱好 3 年,你合資格。如果廣告寫「more than three years」,你就唔合資格。

鋪頭告示。「No more than five items in the express lane。」五件可以;六件唔得。No more than 呢個短語係一個包括邊界數字嘅硬上限。

遊樂設施嘅年齡限制。「Children under 12 ride free。」Under 12 即係嚴格細過 12,所以 11 歲免費,12 歲就唔得。一定要睇清楚個界限有冇包括邊界數字。

煮嘢同節食。「Use at most 200 grams of sugar。」呢個係一個上限:200 克可以接受,201 唔得。對比「use about 200 grams」—— 嗰個容許上下少少嘅彈性。

讀一個圖表標題。「The sample sizes range from n = 30 to n ≥ 100, depending on the study。」讀出嚟:「from n equals thirty to n is greater than or equal to one hundred」。

如果你仲想處理約數同更柔和嘅比較,Around、About、Nearly、Over、Under:英文點樣令數字冇咁精確 解釋 over 同 under 點樣同嚴格嘅不等式符號唔同,以及當一個數 幾乎 —— 但唔完全係 —— 個邊界嗰陣點算。

常犯嘅錯誤

• 將 ≥ 或者 ≤ 淨係讀做 greater than 或者 less than。符號下面嗰條細線好重要 —— 佢包括邊界數字。
• 將 at least 同 or more 疊埋。At least five or more 將同一樣嘢講咗兩次;揀一個。
• 將 no more than 同 at most 疊埋。同一個問題。No more than five at the most 係重複。
• 可數名詞用咗 less。結構係 fewer apples、less water。配數字同金錢,less than five dollars 係標準。
• 講咗 not equals 而唔係 not equal to。否定用形容詞形式:not equal to。
• 混淆 under 12 同 up to 12。Under 12 排除 12。Up to 12 通常包括 12(佢好似一個上限)。當規則重要嗰陣 —— 飛、年齡限制、資格 —— 要睇清楚字眼。
• 喺口語英文將 > 淨係讀做 bigger。Bigger 喺輕鬆傾偈冇問題(「My number is bigger than yours」),但喺技術語境就唔得,嗰度 greater than 係標準。
• 當兩個端點都計嗰陣唔記得標明 inclusive。一個 from 2 to 8 inclusive 嘅範圍同一個 between 2 and 8 exclusive 嘅範圍唔同。

迷你練習

讀出每一行,然後用 at least、at most、more than、less than 或者 between 將佢改寫成淺白英文。

1. x > 10
2. y ≤ 20
3. 5 ≤ z ≤ 9
4. The bus seats no more than 50 passengers.
5. Applicants must be at least 21 years old.

總結

四個不等式符號 >、<、≥ 同 ≤ 對應 greater than、less than、greater than or equal to 同 less than or equal to。喺日常英文,at least 同 at most(或者 no more than)涵蓋包括邊界嘅情況;more than、fewer than、less than、under 同 above 涵蓋排除邊界嘅情況。當規則重要嗰陣 —— 一個測驗、一個年齡限制、一份合約 —— 睇清楚個邊界數字係咪計。一個細細個字就決定咗邊個入、邊個出。

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