グローバルビジネスで役立つ数学（78）奇数、偶数の証明（英語版）

Hi there!

Remember that experience is the best teacher. I’ve learned a lot as a globetrotter traveling worldwide.

Lo and behold, I’ve never run out of steam and been in the doldrums during my stay abroad. I might have been spiritually solid or impervious to all criticisms and dangers, so I had been nominated as a sales representative for several bet-the-company projects.

It goes without saying that the recipe for success in global business is English communication skills. It is true, especially; the more vocabulary you have, the more sensitive message you can deliver. Thanks to my spiritual toughness, I had never felt frustrated by the lack of English expressions while talking with business partners.

The necessity of vocabulary is always deep-rooted in my Business English teachings. That’s why I always give my online students word quizzes. Here is the epitome of my vocabulary question.

Choose the odd one out.
[(A) provisional (B) interim (C) surreptitious (D) tentative (E) caretaker (F) drop-in (G) temporary]

With the above question, you can learn the six words that all mean “Zantei -tekina” except the word “surreptitious” or “Himitsu-no” in Japanese. You should try various measures to memorize new words and change them into an active vocabulary. Devisal is advised.

Today, instead of singling out an odd word, let me challenge a proof problem for odd and even numbers.

Prove whether the following proposition is true or false. If it is false, prove by counterexample. See to it that both \(a\) and \(b\) are integers. Proposition: \(a\) is an odd number, or \(b\) is an odd number if \(a^{2} + b^{2}\) is an odd number. (Source: Yellow Chart Math Ⅰ＋Ａ P80)

Here is my solution to the problem.

Let’s prove its contraposition “\(a^{2} + b^{2}\) is an even number if \(a\) is an even number and \(b\) is an even number.”

Put \(a = 2m\) and \(b = 2n\) (both m and n are integers),
\(a^{2} + b^{2} = (2m)^{2} + (2n)^{2} = 2(2m^{2} + 2n^{2})\)

Since \(2m^{2} + 2n^{2}\) is an integer, \(a^{2} + b^{2}\) becomes an even number.

I don’t know why I was labeled “an odd fish” at my trading company. My matriculation number in high school was also the odd number “23.”

Stay tuned, and expect to see my next post.

Keep well.

Frank Yoshida

￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣
【グローバルビジネスで役立つ数学】でもっと学習する b＾＾)
【参考図書】『もう一度高校数学』（著者：高橋一雄氏）株式会社日本実業出版社
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