How to understand “有理数贯逼近实数”？

Question

In this article, the phrase “有理数贯逼近实数” is used (see the second last paragraph). How to understand this phrase?

Answer 1

"有理数" = rational numbers
"数贯" = (numerical) sequence (obsolete, the more conventional term nowadays is "数列")
"逼近" = literally, "to approach", "to get close to"； mathematically, "to approximate"
"实数" = real numbers

Therefore, "有理数贯逼近实数" means "using a sequence of rationals to approximate (a) real", so this sounds like something similar to a Cauchy sequence.

In context of this article, it is probably that Hua Loo-Keng was giving a lecture on the construction of real numbers using Cauchy sequences (likely in a real analysis course), and he introduced continued fractions (连分数) in the context of that.

Disclaimer: I am a native Chinese (Mandarin) speaker with a reasonable amount of knowledge of mathematics (but I am not a professional mathematician).

Answer 2

Not a math guy, but this is what I found.

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• 有理数 = rational number
• 贯 = sequence
• 逼近 = approximation
• 实数 = real number

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• rational number sequence approximation of a real number

-or- perhaps more colloquially:

• the approximation of real numbers by rational number sequences

Answer 3

It should be understood in this way: 例如/在讲到/用"有理数贯"/逼近"实数"时

where 有理数贯 and 实数 are independent terms.

Answer 4

• “有理数": 可以表达为两个整数比的数 被定义为有理数 (A number that can be expressed as two integer ratios is defined as a rational number)

• 数贯 = suite; sequence (math)

• 有理数贯 = 有理数数贯 (rational number suite/ sequence)

As I see it, 数贯 is another name for 数学公式 (Mathematical formula)

• 逼近 = approach/ close to

• 实数 = real number

“有理数贯逼近实数” means "rational number suite close to a real number"

I think a Mathematician can answer this better. I have no idea what is the difference between rational number and real number and what it meant when he said one is getting close to the other.