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A doorknob of whatever roundish shape is effectively a continuum of levers, with the axis of the latching mechanism—known as the spindle—being the fulcrum about which the turning takes place. Applying a force tangential to the knob is essentially equivalent to applying one perpendicular to a radial line defining the lever.
Equivalent sets should, by rights, have the same "number" of elements. For this reason we sometimes say that equivalent sets have the same cardinality.
2006, Joseph Breuer, Introduction to the Theory of Sets, page 41:
The equivalence theorem: If both M is equivalent to a subset N1 of N and N is equivalent to a subset M1 of M, then the sets M and N are equivalent to each other.
In mathematics, this adjective can be used in phrases like "A and B are equivalent", "A is equivalent to B", and, less commonly, "A is equivalent with B".
Our decision about energy will test the character of the American people and the ability of the President and the Congress to govern. This difficult effort will be the "moral equivalent of war" — except that we will be uniting our efforts to build and not destroy.
Sometimes the noun equivalent to denote a comparable option is assailed for falsely implying absence of difference (false equivalence); when this problem arises, the noun counterpart, or a collocation such as rough equivalent or near equivalent, is sometimes a less misleading choice. In some contexts, the nouns analog or homolog are apt.