Method of successive substitution formula to obtain the solution. Method of successive substitution In modular arithmetic, the method of successive substitution is a method of solving problems of simultaneous congruences by using the definition of the congruence equation. It is commonly applied in cases where the conditions of the Chinese remainder theorem are not satisfied. There is also an unrelated numerical-analysis method of successive substitution, a randomized algorithm used for root finding, an application of fixed-point iteration. The method of successive substitution is also known as back substitution. Consider the simple set of simultaneous congruences Now, for "x" ≡ 3 (mod 4) to be
How many angels can dance on the head of a pin? dancing on a needle's point occurs in an expository work by the English divine, William Sclater (1575-1626). In "An exposition with notes vpon the first Epistle to the Thessalonians" (1619), Sclater claimed that scholastic philosophers occupied themselves with such pointless questions as whether angels "did occupie a place; and so, whether many might be in one place at one time; and how many might sit on a Needles point; and six hundred such like needlesse points." Harrison proposes that the reason an English writer first introduced the "needle’s point" into a critique of medieval angelology is that it makes for