Math
I have put the Algebra info on here:
I haven't seen alot of Algebra programs for computers, but I am sure they have some.
Algebra in Databases JR Wyatt
For Fractions each number, the one above the line and the one below the line should be entered seperate then from that you can simplify in Algebra or make it into a decimal.
Also the Parentisis should be entered separate and thus the distributive law can be utilized Algebraicly
A(B+C) = AB + AC Calculators are normally only used when there are no variables meaning all numbers are known. So the Function input itself + - / x Should be put through a Logic Sequence to see if the Parentisis should be dropped Associative Law Style A(BC) = A.B.C read A times B times C multiplication. Logic can be used too if each Character is entered into a seperate Field within a database. The Code Required could be considered Lengthy but it would simplify with "If Then Statements" I have a example that I might be able to show you in the future.
In that example two variables are used thus an extra character would need to be used to denote a factor (to the Power) Ie. X to the power of 2 , X to the power of 3, X to the power of 4, Ect. Possibly use R because ABC and XYZ are seen alot in Variable Calculating. Use R with Parentisis or Brackets to denote a bracket that stretches into 2 spaces mabey use S to denote parentisis or Brackets that stretch 3 spaces vertical. But remember a factor is within one space vertical but utilizes 2 spaces horizontal with a R denotation therefore every number will require a blank space beside it or an R icluding spaces for Brackets and Paretisis. Remember the order in Logic Brackets First, Parentisis Second. 3 over A Minus A over -3 equal to A-3 over -3 + A should cancel each other out. And a -1 should change the sign if multiplied. Both sides can be multiplied by -1 also. If a Negative Number is in denominator multiply numerator and denominator by -1 then multiply.
For Common Mathmatics the Decimal System
is used with base ten.
Other bases are sometimes used such as bianary, hexadecimal, and octaldecimal;
any bianary diget can be replaced by a three diget octaldecimal diget or a four diget hexadecimal diget.
Sets:
{ } [ ] Brackets, Braces denotes sets.
A Large E shaped symbol denotes an element belongs to a set a E S a belongs to set S.
A line drawn through such a symbol of course means does not belong. I will substitute a alt+y symbol¥ a ¥ S a does not belong to set S.
If a set contains only one element it is a constant.
A Large U Shape symbol denotes a universal set in which all elements under consideration exist and belong.
A 0 denotes an empty set or empty braces [ ]
A Large sideways U pointed to the left denotes blank is a proper subset of blank. C can be used.
ACB A=B And if these two statements are true along with the two being = then they are combined as a symbol and written AC_B "the _ should actually be directly under the large sideways U (which looks like a C here)"
There are also lapping and disjoint subsets.
A VENN Diagram is a visual representation of the sets and subsets.
~ denotes equivalence but this typewritten version here is a bit small and sometimes is printed a little high. A actual capital U is used to denote unison but since we are using U already to act as a Universal set I recommend using a small u.
Number Systems
Real Numbers All Rational and Irrational Numbers. Intergers-Positive Numbers , Negative Numbers , and 0. Natural Numbers 1 and Higher. Whole Numbers 0 and Natural Numbers.
Rational Numbers are Terminating and Repeating Decimals. Irrational Numbers are Non Terminating Decimals.
Complex Numbers are created by adding a real number to an imaginary number.
An Imaginary Number is the square root of a negative 1. There are also Polygonal, Triangle, Square, Pentagonal Numbers.
Factors
A proper factor is a natural number less than a number which divides evenly into it. Proper factors of 8 are 1,2, and 4.
only 1 will divide into a prime number.
Prime Numbers to 101 are: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,and 101.
Real Numbers
Four Properties of equality
1 a=a Reflective
2 If a=b b=a Symmetric "Order is Interchangeable"
3 If a=b b=c a=c Transitive
4 If a=b b=c a=c Substitutable
11 Axioms