Search results
Results from the WOW.Com Content Network
Modern texts, that define fields as a special type of ring, include the axiom 0 ≠ 1 for fields (or its equivalent) so that the zero ring is excluded from being a field. In the zero ring, division by zero is possible, which shows that the other field axioms are not sufficient to exclude division by zero in a field.
This is because if b were a negative number then dividing by a negative would change the ≥ relationship into a ≤ relationship. For example, although 2 is more than 1, –2 is less than –1. Also if b were zero then zero times anything is zero and cancelling out would mean dividing by zero in that case which cannot be
In arithmetic, and therefore algebra, division by zero is undefined. [7] Use of a division by zero in an arithmetical calculation or proof, can produce absurd or meaningless results. Assuming that division by zero exists, can produce inconsistent logical results, such as the following fallacious "proof" that one is equal to two [ 8 ] :
The report implied that Anderson had discovered the solution to division by zero, rather than simply attempting to formalize it. The report also suggested that Anderson was the first to solve this problem, when in fact the result of zero divided by zero has been expressed formally in a number of different ways (for example, NaN ).
In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
There can be confusion between 0- and 1-based indexing; for example, Java's JDBC indexes parameters from 1 although Java itself uses 0-based indexing. [89] In C, a byte containing the value 0 serves to indicate where a string of characters ends. Also, 0 is a standard way to refer to a null pointer in code. [90]
Now we have a number smaller than 7, and this number (4) is the remainder of dividing 186/7. So 186 minus 4, which is 182, must be a multiple of 7. Note: The reason why this works is that if we have: a+b=c and b is a multiple of any given number n, then a and c will necessarily produce the same remainder when divided by n. In other words, in 2 ...