10,000 (ten thousand) is the natural number following 9,999 and preceding 10,001. In scientific notation, it is expressed as $10^4$.
Mathematical Properties
10,000 is an even composite number. It is the square of 100 ($100^2$) and the square root of 100,000,000. In the decimal system, it is the smallest five-digit number. While the International System of Units (SI) uses prefixes based on powers of 1,000, the prefix "myria-" was historically used to represent a factor of 10,000, though it is now obsolete.
Etymology and Terminology
In Ancient Greek, the number 10,000 is known as a myriad (μυριάς). In English, while "myriad" technically denotes 10,000, it is more commonly used as a figure of speech to signify an indefinitely large number.
In East Asian numeral systems—including Chinese, Japanese, and Korean—10,000 (Chinese: 万/萬; pinyin: wàn; Japanese: man; Korean: man) serves as a foundational unit of counting. Unlike Western systems that group numbers by thousands ($10^3$), these systems group numbers by ten-thousands ($10^4$). Consequently, larger numbers are often described in multiples of 10,000 rather than 1,000.
Historical and Literary Significance
- The Ten Thousand: This term historically refers to a group of Greek mercenary units employed by Cyrus the Younger in 401 BC during his attempt to seize the Persian throne. Their subsequent retreat across Asia Minor was chronicled by the soldier and historian Xenophon in the Anabasis.
- The Immortals: In the Achaemenid Empire, the "Immortals" were an elite corps of 10,000 soldiers. The name derived from the practice of immediately replacing any killed or disabled member to maintain the force exactly at 10,000 men.
- Longevity Symbolism: In various East Asian cultures, the phrase "ten thousand years" (e.g., Banzai in Japanese, Wansui in Chinese) is used as an exclamation to wish for long life or the eternal prosperity of a ruler or nation.
Practical Applications
- Finance: Many currencies have issued banknotes in denominations of 10,000, such as the Japanese 10,000 yen note.
- Computing: In digital imaging and data, 10,000 is often a round number used for limits or benchmarks.
- Public Health: A goal of 10,000 steps per day is frequently cited in fitness and health guidelines as a target for physical activity, a figure originally popularized by a Japanese marketing campaign for pedometers in the 1960s.
