# How to understand “有理数贯逼近实数”？

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?

"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).

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

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

• rational number sequence approximation of a real number

-or- perhaps more colloquially:

• the approximation of real numbers by rational number sequences
• 逼近 is, apparently, not a noun word in this context.
– dan
Jan 31 '19 at 6:31
• 逼近 is defined by Grand Ricci as `(Math.) Approximation. `
– Mou某
Jan 31 '19 at 6:32
• It could be either "approximate" or "approximation", depending on how you use it.
– dan
Jan 31 '19 at 6:36
• 贯 looks strange to me in this sentence.
– iBug
Jan 31 '19 at 9:37

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.

• 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.

• 实数 should be real number
– fefe
Jan 31 '19 at 6:17
• that show how little I know math. 'real ' and 'actual ' seem like the same to me at first, now I see 'actual number' could mean 'exact number'
– Tang Ho
Jan 31 '19 at 6:22