Noun:

प्रमेयोपपाद्य, उपपाद्य,

theorem's Usage Examples:

is approximately equal to -J(27rn).(nle) n; the approximation may be improved by Stirling's theorem log e 2 +log e 3 +...

It has been mentioned in � 41 (ix.) that the binomial theorem can be used for obtaining an approximate value for a power of a number; the most important terms only being taken into account.

We therefore have the fundamental theorem that the angular velocity of the body around the centre of attraction varies inversely as the square of its distance, and is therefore at every point proportional to the gravitation of the sun.

This theorem is due to Cayley, and reference may be made to Salmon's Higher Algebra, 4th ed.

By means of this theorem it can be shown that, whatever the value of n may be, f 1 + (plq)(i)x+(p/q)(2)x2+...

This theorem was investigated by Sir W.

These laws can be established either by tracing the individual terms in a sum or a product or by means of the general theorem in � 52 (vi.).

Consideration of the binomial theorem for fractional index, or of the continued fraction representing a surd, or of theorems such as Wallis's theorem (� 64), shows that a sequence, every term of which is rational, may have as its limit an irrational number, i.e.

This is the binomial theorem for a positive integral index.

This is the true standpoint from which the theorem should be regarded.

Synonyms:

binomial theorem, proposition,

Antonyms:

particular proposition, particular, unbelief,