40

No. Japanese "haute cuisine" is called 懐石(料理). Mathematical analysis is 解析(学). What is true is that 懐石 and 解析 are homophones, both pronounced かいせき and, in context, both may be referred to as かいせき. However, they are not the same word. By the way, there are more homophones for かいせき, so he could have also said that "analysis" is the "same word" as bizarre ...


29

First of all, let me assume: You're only interested in the simple four operations (+, -, *, /) and brackets ( ) Multiplication and division have higher priority, e.g., 1 + 2 * 3 is 7, not 9 Of course you want to make the reading unambiguous, taking brackets into consideration So we want to read something like 1 + 3 * (4 - 1) (=10) but nothing more ...


23

+: 足{た}す -: 引{ひ}く /: 割{わ}る *: 掛{か}ける And you just say the terms normally in order. So your example of 3 * 4 = 12 would be 3かける4は12. Note that = becomes は, similar to how we use "is" in English. As @blutorange mentioned, you can use イコール to mean "equals," however in most situations you'll be good using は. You learn these things quickly when listening to ...


23

While the pronunciation is the same, the words' etymologies are unrelated. Mathematical analysis is 解析(kaiseki かいせき) while (Japanese) fine cuisine is 懐石(kaiseki かいせき). Both 解 and 析 roughly stands for "understanding", "taking apart". For example, 解説(kaisetu) means "To orally explain", 分析(bunseki) means "To analyze". On the other hand, 懐(kai) refers to ...


12

They are not grammatical phrases. We just read the symbols verbatim like: [⁠1]{いち} [+]{たす} [⁠2]{に} [=]{は} [⁠3]{さん} It has nothing different than saying: [⁠1]{いち} [+]{プラス} [⁠2]{に} [=]{イコール} [⁠3]{さん} which is also commonly heard. Though we have both [+]{たす/プラス} and [−]{ひく/マイナス}, [×]{かける} and [÷]{わる} only have native pronunciations. See this link for common ...


12

R → ∞ is usually read R を限りなく大きくする[と・とき] R が限りなく大きくなる[と・とき] I don't think that 「R → ∞ のとき」 is supposed to have a fixed natural pronunciation. You can ignore the の and read it as above, or you could probably read it as [R]{アール} [→]{トゥ} [∞]{インフィニティ} のとき [R]{アール} [→]{ツー} [∞]{インフィニティ} のとき


12

Two common ways of translating "if and only if" use the terms 必要十分条件 ("necessary and sufficient condition") and 同値 ("equivalence"). a > b は式 (15) である為の必要十分条件である。 Equation (15) holds if and only if a > b. 式 (15) と「a>b」とは同値である。 Equation (15) is equivalent to a > b.


12

As Gradius said, the mathematical term “triangle” is 三角形, and never 三角. As part of compound words, 三角 also appears; an example is 三角関数 (trigonometric functions). (As for the use of 三角 in compounds words, I think that there is a general tendency to prefer to two-kanji words than three-kanji words when they are used adjectivally in compound words. See also ...


11

A distinction is usually made between positional numeral systems and non-positional. Let's use Arabic numerals as an example of a positional numeral system. In this kind of system, if we write 100, each digit represents a coefficient in an exponential series. Let's use b to represent the base: 1b2 + 0b1 + 0b0 = 100 Okay, so what about 漢数字? The numbers ...


10

Here are some facts, and my speculations. Actual Usuages Japanese as Text In non-technical context, we can use arbitrary text (just like in English) in equations: 長方形について, "面積 = 縦 × 横" is a natural way of expressing the idea (so is "area = length × width"). Elaborating on this, 仕事 = ∫ 力・d(位置) is very rarely seen but would be ...


9

You can read the arithmetic operators as follows:    +   たす    (足す)    -   ひく    (引く)    ×   かける   (掛ける)    ÷   わる    (割る) In place of the equals sign, you'd most likely use a particle such as は, much as we might say "three times four is twelve" in English to make a complete sentence out of it. Your example looks like this:   3   ×   4 = 12   さん、かける、よんは、...


8

I think you're asking this because in English, we distinguish times from by: 3×3=9         three times three is nine a 3×3 block      a three-by-three block But I think in Japanese, it's just かける in both cases: 3×3=9     さんかけるさんはきゅう 3×3のブロック  さんかけるさんのブロック You can see that both uses are listed on Wikipedia's article for × in the same section (titled 積), ...


8

Please read this first: Standard mathematical operations, expressed in Japanese As described in the question above, there are several approaches to read this. The most simple approach is to read each symbol one by one. This ^ symbol can be read ハット, キャレット or 累乗【るいじょう】. かっこ エックス たす ワイ かっことじ るいじょう ゼット More naturally, the expression xn can be read as "xのn乗"...


7

You're taking the third place (第3位) and you're either throwing it away if it's four or below (四捨) or you add one to the next place if it's five or above (五入). As a result, the third place is gone, and you're only left with two decimal places.


7

It might be something as simple as: 三角 (something that is "triangular" where the focus is having attributes similar to that of triangles ie: three sides, three corners) 三角形 (a polygon that IS a triangle) For example: 「三角屋根」 is a way to describe a roof that is "triangular" in comparison to other roofs of different shapes. It has attributes similar to ...


7

In the context of mathematics, 「高々 (or たかだか) 一個」 is the standard expression. 高々 can also be used in non-technical context, but it's somewhat formal. In daily conversations, we'd say "多くて(も)一個" or "最大で一個", etc.


7

Not exactly (as several have commented). This is how you talk about fractions in Japanese: 7分の1 → 1/7 Literally, you can think about it as 'one part of seven'. It is not a ratio, i.e. 'one part to seven parts', as that equates to 1/8.


7

Japan uses 「足す」(tasu:plus)「引く」(hiku:minus)「掛ける」(kakeru:multiplied by)「割る」(waru:divided by). For example, 2+2 in words is "ni tasu ni", 2-2 is "ni hiku ni", 2x2 is "ni kakeru ni", 2/2 is "ni waru ni". If it is assumed that the person using the calculator program is a native Japanese speaker, I think they will be more comfortable using those four terms rather ...


6

The sentence-final copula である ("be") is almost always omitted because it's obvious in definitions, leaving the sentences looking like ending with nouns. Both もの and こと are frequently used nominalizers translating "what do ~" and "doing ~" respectively. すなわち、1. (...) 2. (...) となるもの。 i.e. what satisfies 1. (...) and 2. (...). f:S→T が全射であるとは、f(S)=T ...


6

証拠立てる is virtually never used in mathematical articles. I would translate it like so: すべてのxに対してP(x)が真であることを示せ。 すべてのxについてP(x)が成り立つことを証明せよ。


6

if and only if (= iff) a > b の時、(そして/かつ)その時に限り等式が成立する。 The equation is satisfied if and only if a > b. only ... if ~なければ~ない (colloquially ~なきゃ~ない or ~なけりゃ~ない) ≈ ~ないなら~ない アイスを買ってくれなきゃ行かない。 I'll only go if you buy me an ice. ~ないと~ない この植物は定期的に水をやらないと育たない。 The plant will only grow if it is watered regularly. The difference between them ...


6

As @naruto notes, the difference between Tôhoku and Tōhoku is only a difference of romanization systems. (Both are correct transliterations of 東北 in their respective systems.) A number of romanization systems are used in Japan, so Japanese speakers will probably not give it a second thought. Presumably the reason that the paper is referred to as the Tôhoku ...


6

In Japanese, there are two sets of words we learn to describe various kinds of quadrilaterals. Mathematical terms are 四角形【しかっけい】 quadrilaterals, 台形【だいけい】 trapezoid, 平行四辺形【へいこうしへんけい】 parallelogram, 菱形【ひしがた】 rhombus, 長方形【ちょうほうけい】 rectangle and 正方形【せいほうけい】 square. Some are specialized forms of others, as shown below: If I remember correctly, Japanese people ...


5

The correspondence isn't direct; if 位相幾何学 were loan translated into English it would be 位相 (topological) 幾何学 (geometry). Interestingly, though, 位相 means phase (i.e. of a sinusoidal function) as well as topology, and that means that the term 位相空間 is ambiguous between phase space (in physics) and topological space (in mathematics). EDIT: To clarify the ...


5

Numbers written in kanji are analogous in English to numbers written out in full. The joke would be just as ruined in English if it were written "There are only ten types of people..."


5

In Japanese, R is pronounced aaru (アール) → is pronounced yajirusi (矢印【やじるし】) ∞ is pronounced mugendai (無限大【むげんだい】) I think "n→∞" is often pronounced as follows in the differential and integral. エヌ矢印無限大 enu yajirusi mugendai エヌ無限大 enu mugendai where enu (エヌ) means the letter N. Therefore I guess that "R→∞" is pronounced in the same way. Although, because ...


5

(3 + 1 - 2) * 6 / 2 How about... SAN tasu ICHI hiku NI, kakeru ROKU waru NI (or SAN purasu ICHI mainasu NI, kakeru ROKU waru NI) We usually read the parentheses (in maths) as "kakko ... kakko tojiru", as in: (3 + 1 - 2) * 6 / 2 kakko SAN tasu ICHI hiku NI kakko tojiru kekeru ROKU waru NI though it might look a bit wordy...


4

≦ is used everywhere in Japan, unless it's a paper written in English.


4

Find here http://ejje.weblio.jp/content/negation 4)〔数学〕否定, 相反《真偽を逆にした命題》.


4

I think I learnt in elementary math that 22 % 3 = 1 would be read as 22を3で割るところの余りは1 Hence, I would read the example in the original question as 4を2で割るところの余りは0


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