An inscription made in 876 at Gwalior, India, contains a symbol indicating the absence of a number, but the Indians, like the contemporary Mayans and the classical Greeks and Romans, do not make mathematical use of such symbols.

Thus, the introduction of zero into Arabic and Hindu mathematics as an actual working tool is a revolutionary development.

Abu Ishaq Ibrahim is the son of the Aghlabid emir Ahmad of Ifriqiya.

After his father's death in 863, the emirate of Ifriqiya had passed to his father's brother Ziyadat Allah II, but he died shortly after, and the succession had passed back to the main line, to Ibrahim's brother Abu 'l-Gharaniq Muhammad II, who proves to be a frivolous and pleasure-loving ruler.

During his brother's emirate, Ibrahim had been assigned the governorship of Kairouan, an office he had executed with exemplary efficiency and seriousness, which had earned him much admiration.

Hopes were high when the dissolute Muhammad II died prematurely in February 875 and the emirate had passed to Ibrahim II, his candidacy pushed forward by popular crowds and endorsed by the jurists of Kairouan, who had set aside the claims of his young nephew, the son of Muhammad II.

Although Ibrahim II had inherited a kingdom depopulated by the plague of 874, his reign is economically prosperous.

He revives the religious police and is said to have rid the roads of banditry and secured the safety of commerce.

He seeks to develop agriculture by building up the irrigation system.

Among his public works, Ibrahim completes the Zaytuna mosque of Tunis, enlarges the Uqba mosque of Kairouan, builds a vast new water reservoir for the city, erects the walls of Sousse, and establishes a line of new naval signal towers along the Ifriqiyan coast (it reportedly takes one night to dispatch a message from Ceuta in Morocco to Alexandria in Egypt).

Louis is preparing for war when he dies at Frankfurt on August 28, 876.

He is buried at the abbey of Lorsch, leaving three sons and three daughters.

His sons, unusually for the times, respect the division made a decade earlier and each contents himself with his own kingdom.

Considered by many to be the most competent of the grandsons of Charlemagne, Louis in the face of the attacks of Vikings, Slavs, and others had obtained for his kingdom a certain degree of security.

He lived in close alliance with the Church, to which he was very generous, and entered eagerly into schemes for the conversion of his heathen neighbors.

Halfdan moves north to attack the Picts, while Guthrum emerges as the war leader in the south; joined in 876 by additional forces, they win the Battle of Wareham.

The town of Swanage, first mentioned in historical texts in the Anglo-Saxon Chronicle of 877, is stated as being the scene of a great naval victory by King Alfred over the Danes: "This year came the Danish army into Exeter from Wareham; whilst the navy sailed west about, until they met with a great mist at sea, and there perished one hundred and twenty ships at Swanwich."

A hundred Danish ships that had survived the battle are driven by a storm onto Peveril Point, a shallow rocky reef outcropping from the southern end of Swanage Bay.

Svatopluk distinguishes himself in the conduct of political affairs.

After the death of Louis the German in 876, Svatopluk acquires large territories with Slavic populations.

The Great Moravia that he creates includes all of Bohemia, the southern part of modern Poland, and the western part of modern Hungary.

He annexes some territories and leaves local princes who recognize his suzerainty in others.

Such is apparently the case of the Czech prince Borivoj I. Propagation of Christianity follows Svatopluk's advances.

According to legends, Borivoj is baptized by Methodius and then admits clerics of the Slavic rite to his principality.

While the archbishop is engaged in missionary work in the annexed territories, however, advocates of the Latin rite, headed by a Frankish cleric, Wiching, bishop of Nitra, strengthen their position in Moravia.

Huang Chao subsequently roams throughout central China, and his campaign takes him into many engagements with Tang forces.

In spring 877, Huang captures Tianping's capital Yun Prefecture, killing Xue Chong, then captures Yi Prefecture (in modern Linyi, Shandong).

Huang joins forces with Shang Junzhang's brother Shang Rang at Mount Chaya (in modern Zhumadian, Henan) in summer 877.

He and Wang Xianzhi then briefly join forces again and put the Tang general Song Wei under siege at Song Prefecture (in modern Shangqiu, Henan).

However, the Tang general Zhang Zimian then arrives and defeats them, and they lift the siege on Song Prefecture and scatter.

Huang pillages Qi and Huang (in modern Wuhan, Hubei) Prefectures in winter 877, but flees after the Tang general Zeng Yuanyu defeats him.

Huang soon captures Kuangcheng (in modern Xinxiang) and …