基底|きていkitei[0]heiban (flat)

1. nounbase; basis; foundation
   そして記念碑きねんひの基底きてい部分ぶぶんには願い事ねがいごとが刻きざまれている。↗

   And a wish is engraved on the base of the statue.
2. noun, mathbasis (linear algebra)
3. noun, mathbase (topology); basis

• Synonym元もとNeutralThe most common everyday choice: origin, cause or basis, with the widest range. 「基底」 is a written word for the underlying foundation at the root of something.
• Synonym根本こんぽんNeutralRead the same as 「根元」, 「ねもと」: mainly the part of a trunk or pillar that touches the ground, or hair roots; also a problem's root. 「基底」 is the underlying basis.
• Synonym基部きぶWrittenWritten term for the lower end of a building, pillar, component or organ. Strictly a physical part, while 「基底」 can also be an abstract foundation.
• Synonym基礎きそNeutralThe everyday word for foundations, physical or in learning, as in 「基礎知識」. 「基底」 is written style and points to a deeper, underlying basis.
• Synonym下したNeutralThe everyday word for 'below', as in 「机の下」. It never means a foundation; it meets 「基底」 only where both suggest the bottom position.
• Synonym根底こんていWrittenWritten word for the deep roots of ideas or systems, as in 「根底から覆す」. Close to 「基底」 in sense but more frequently used.
• Synonym土台どだいNeutralA physical base or footing that carries the weight above, also used figuratively, as in 「土台作り」. More concrete and colloquial than 「基底」.
• Synonym根っこねっこCasualColloquial for plant roots or the heart of a problem, as in 「問題の根っこ」. Homely in tone, while 「基底」 belongs to written prose.
• Synonym礎いしずえWrittenWritten and solemn: the stone built into a building's base, figuratively the foundation of an undertaking, as in 「国の礎」. 「基底」 is plainer, more expository.
• Synonym礎石そせきWrittenWritten word for the stone beneath a pillar, figuratively a basis as well. The image stays stone-concrete; 「基底」 is the underlying basis or a solid's base.
• Synonym基本きほんNeutralEveryday word for the basics or essentials to master, as in 「基本的な考え」. 「基底」 is written style and leans toward a deep underlying basis.
• Synonym基盤きばんNeutralThe footing an activity needs to stand on, as in 「生活基盤」; mostly social and economic contexts. 「基底」 suits thought and geometry.
• Synonym底そこNeutralThe lowest part of a pot, landform or the like, as in 「鍋の底」. Here it leans toward the concrete bottom, overlapping with 「基底」 only in the base-surface sense.
• Synonym根ねNeutralA plant's root, figuratively the source of a problem, as in 「悪の根」. It points to the origin; 「基底」 points to the underlying basis.
• Synonym下地したじNeutralGroundwork laid beforehand: aptitude or training one already has, or an undercoat of paint, as in 「下地がある」. 「基底」 is the fundamental basis itself.
• Synonym底辺ていへんWrittenWritten term for the base edge of a polygon, also the bottom of society. In geometry it corresponds to 「基底」's base face but names only the edge.
• SynonymベースNeutralLoanword for basis, standard or a base; wide-ranging and common in speech. 「基底」 is the written choice, seen in essays and mathematics.
• Synonym根元ねもとNeutralThe base of a tree or pillar where it meets the ground, or hair roots; also a problem's root. More colloquial than 「基底」, never a geometric base.
• Synonym底面ていめんWrittenWritten term for the bottom face of a solid or object. Near 「基底」 in the geometric sense, but it never means an abstract foundation.
• Synonym最下部さいかぶWrittenWritten word for the lowest part of a page, screen or object. Purely positional, while 「基底」 can also name the fundamental basis.
• Synonym底部ていぶNeutralThe bottom part of an object, as in 「容器の底部」. It stays with physical position; 「基底」 can also be an abstract foundation.
• Related下したNeutralThe everyday word for 'below', as in 「机の下」. It never means a foundation; it meets 「基底」 only where both suggest the bottom position.
• Related根源こんげんWrittenWritten word for the root cause something springs from, as in 「諸悪の根源」. It stresses the causal source; 「基底」 stresses the underlying basis.
• Antonym頂点ちょうてんNeutralAntonym: the highest point, or the vertex of a figure. It stands at the opposite end from 「基底」, which sits at the very bottom.

In written prose, 「基底」 names the underlying basis at the root of something or a geometric base, as in 「思想の基底」. For everyday foundations reach for 「基礎」 or 「土台」; for deep-seated roots, 「根底」.

Usage comparisons are AI-assisted and cross-checked by multiple models; for study reference only

1. ある物事ものごとの大本おおもとを与あたえるもっと基礎的きそてきな物事ものごと。
2. 立体的りったいてきな物体ぶったいの底面ていめん。
3. （数学すうがく）あるベクトル空間くうかん上じょうの任意にんいのベクトルを張はることができる一いち次じ独立どくりつなベクトルの組くみ。n 次元じげんベクトル空間くうかん上じょうの一いち次じ独立どくりつな n 個このベクトルの組くみ。