一日一善 is a Chinese, Japanese Kanji, and old Korean Hanja phrase that suggests doing a good deed each day or doing one good turn a day.

It literally reads, “One Day, One Good (Deed).”

This Chinese word means to progress, increase, or change day by day.

It suggests something getting better one day at a time or with each passing day.

一日千秋 is a Japanese and Chinese proverb about missing someone.

一日千秋 is often used to express how hard it is to wait for someone's return or to be away from someone.

Some will translate this as “one day feels like a very long time” or “waiting for someone (something) is hard.”

You might see this romanized as a single word, Ichijitsusenshuu, or as “Ichijitsu Senshuu” from Japanese.
If you break down the characters one-by-one, we get:
一 = one/a
日 = day/sun (can also represent time or date)
千 = 1000/thousand
秋 = autumn/fall

Together, 千秋 can mean “autumn comes thousand times” (or 1000 years). It can also be read as 1000 periods of time.
However, it relays the idea of heartache as you wait for someone you miss.

Long ago in what is now China, there were many kingdoms throughout the land. This time period is known as “The Warring States Period” by historians because these kingdoms often did not get along with each other.

Sometime around 279 B.C. the Kingdom of Chu was a large but not particularly powerful kingdom. Part of the reason it lacked power was the fact that the King was surrounded by “yes men” who told him only what he wanted to hear. Many of the King's court officials were corrupt and incompetent which did not help the situation.

The King was not blameless himself, as he started spending much of his time being entertained by his many concubines.

One of the King's ministers, Zhuang Xin, saw problems on the horizon for the Kingdom, and warned the King, “Your Majesty, you are surrounded by people who tell you what you want to hear. They tell you things to make you happy and cause you to ignore important state affairs. If this is allowed to continue, the Kingdom of Chu will surely perish, and fall into ruins.”

This enraged the King who scolded Zhuang Xin for insulting the country and accused him of trying to create resentment among the people. Zhuang Xin explained, “I dare not curse the Kingdom of Chu but I feel that we face great danger in the future because of the current situation.” The King was simply not impressed with Zhuang Xin's words.
Seeing the King's displeasure with him and the King's fondness for his court of corrupt officials, Zhuang Xin asked permission from the King that he may take leave of the Kingdom of Chu, and travel to the State of Zhao to live. The King agreed, and Zhuang Xin left the Kingdom of Chu, perhaps forever.

Five months later, troops from the neighboring Kingdom of Qin invaded Chu, taking a huge tract of land. The King of Chu went into exile, and it appeared that soon, the Kingdom of Chu would no longer exist.

The King of Chu remembered the words of Zhuang Xin and sent some of his men to find him. Immediately, Zhuang Xin returned to meet the King. The first question asked by the King was “What can I do now?”

Zhuang Xin told the King this story:

A shepherd woke one morning to find a sheep missing. Looking at the pen saw a hole in the fence where a wolf had come through to steal one of his sheep. His friends told him that he had best fix the hole at once. But the Shepherd thought since the sheep is already gone, there is no use fixing the hole.
The next morning, another sheep was missing. And the Shepherd realized that he must mend the fence at once. Zhuang Xin then went on to make suggestions about what could be done to reclaim the land lost to the Kingdom of Qin, and reclaim the former glory and integrity of the Kingdom of Chu.

The Chinese idiom shown above came from this reply from Zhuang Xin to the King of Chu almost 2,300 years ago.
It translates roughly into English as...
“Even if you have lost some sheep, it's never too late to mend the fence.”

This proverb, 亡羊补牢犹未为晚, is often used in modern China when suggesting in a hopeful way that someone change their ways, or fix something in their life. It might be used to suggest fixing a marriage, quitting smoking, or getting back on track after taking an unfortunate path in life among other things one might fix in their life.

I suppose in the same way that we might say, “Today is the first day of the rest of your life” in our western cultures to suggest that you can always start anew.

Note: This does have Korean pronunciation but is not a well-known proverb in Korean (only Koreans familiar with ancient Chinese history would know it). Best if your audience is Chinese.

During the Tang Dynasty, a man named Jia Dao (born in the year 779), a well-studied scholar and poet, went to the capital to take the imperial examination.

One day as he rides a donkey through the city streets, a poem begins to form in his mind. A portion of the poem comes into his head like this:

“The bird sits on the tree branch near a pond,
A monk approaches and knocks at the gate...”

At the same time, he wondered if the word “push” would be better than “knock” in his poem.

As he rides down the street, he imagines the monk pushing or knocking. Soon he finds himself making motions of pushing and shaking a fist in a knocking motion as he debates which word to use. He is quite a sight as he makes his way down the street on his donkey with hands and fists flying about as the internal debate continues.

As he amuses people along the street, he becomes completely lost in his thoughts and does not see the mayor's procession coming in the opposite direction. Jia Bao is blocking the way for the procession to continue down the road, and the mayor's guards immediately decide to remove Jia Bao by force. Jia Bao, not realizing that he was in the way, apologizes, explains his poetic dilemma and awaits his punishment for blocking the mayor's way.

The mayor, Han Yu, a scholar and author of prose himself, finds himself intrigued by Jia Dao's poem and problem. Han Yu gets off his horse and addresses Jia Bao, stating, “I think knock is better.” The relieved Jia Bao raises his head and is invited by the mayor to join the procession, and are seen riding off together down the street, exchanging their ideas and love of poetry.

In modern Chinese, this 反復推敲 idiom is used when someone is trying to decide which word to use in their writing or when struggling to decide between two things when neither seems to have a downside.