Etymology
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step (v.)

Old English steppan (Anglian), stæppan (West Saxon) "take a step," from West Germanic *stap- "tread" (source also of Old Frisian stapa, Middle Dutch, Dutch stappen, Old High German stapfon, German stapfen "step"), from PIE root *stebh- "post, stem; to support, place firmly on" (see staff (n.); source also of Old Church Slavonic stopa "step, pace," stepeni "step, degree"). The notion is perhaps "a treading firmly on; a foothold."

Transitive sense (as in step foot in) attested from 1530s. Related: Stepped; stepping. Originally strong (past tense stop, past participle bestapen); weak forms emerged 13c., universal from 16c. To step out "leave for a short time" is from 1530s; meaning "to go out in public in style" is from 1907. Step on it "hurry up" is 1923, from notion of gas pedal.

step (n.)

Old English steppa (Mercian), stæpe, stepe (West Saxon) "stair, act of stepping," from the source of step (v.). Compare Old Frisian, Middle Dutch, Dutch stap, Old High German stapfo, German Stapfe "footstep"). From late Old English as "degree on a scale." Figurative meaning "action which leads toward a result" is recorded from 1540s. In dancing, from 1670s. Meaning "type of military pace" is from 1798. Warning phrase watch your step is attested from 1911 (Wyclif (late 14c.) has keep thy foot in essentially the same sense). Step by step indicating steady progression is from 1580s. To follow in (someone's) steps is from mid-13c.

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Definitions of step
1
step (n.)
any maneuver made as part of progress toward a goal;
the police took steps to reduce crime
Synonyms: measure
step (n.)
the distance covered by a step;
he stepped off ten paces from the old tree and began to dig
Synonyms: footstep / pace / stride
step (n.)
the act of changing location by raising the foot and setting it down;
he walked with unsteady steps
step (n.)
support consisting of a place to rest the foot while ascending or descending a stairway;
he paused on the bottom step
Synonyms: stair
step (n.)
relative position in a graded series;
keep in step with the fashions
always a step behind
Synonyms: gradation
step (n.)
a short distance;
it's only a step to the drugstore
Synonyms: stone's throw
step (n.)
the sound of a step of someone walking;
Synonyms: footfall / footstep
step (n.)
a musical interval of two semitones;
Synonyms: tone / whole tone / whole step
step (n.)
a mark of a foot or shoe on a surface;
Synonyms: footprint / footmark
step (n.)
a solid block joined to the beams in which the heel of a ship's mast or capstan is fixed;
step (n.)
a sequence of foot movements that make up a particular dance;
he taught them the waltz step
Synonyms: dance step
2
step (v.)
shift or move by taking a step;
step back
step (v.)
put down or press the foot, place the foot;
step on the brake
Synonyms: tread
step (v.)
cause (a computer) to execute a single command;
step (v.)
treat badly;
She is always stepping on others to get ahead
Synonyms: mistreat / maltreat / abuse / ill-use / ill-treat
step (v.)
furnish with steps;
The architect wants to step the terrace
step (v.)
move with one's feet in a specific manner;
step lively
step (v.)
walk a short distance to a specified place or in a specified manner;
step over to the blackboard
step (v.)
place (a ship's mast) in its step;
step (v.)
measure (distances) by pacing;
step off ten yards
Synonyms: pace
step (v.)
move or proceed as if by steps into a new situation;
She stepped into a life of luxury
From wordnet.princeton.edu