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Branch of Mathematics |
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Mathematics |
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ALGEBRA Series(special)
GEOMETRY Theoretical Geometry Constructions Applied geometry
TRIGONOMETRY Angles and measures Trigonometric Ratio Algebra of T-functions Properties of triangles Applied Trigonometry
CALCULUS Examples of different kinds of functions Graph of functions Limit of a function Continuity of a function Differential Calculus Integral Calculus Applied Calculus
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The following are the mathematical numbers: 1. Natural Numbers. 2. Whole Numbers 3. Integers 4.
Rational Numbers and Irrational Numbers 5. Real Numbers 6. Complex Numbers 7.
Numbers beyond complex... 8 Infinity .Let us learn facts: INDIAN NUMBER SYSTEM
ENGLISH NUBER SYSTEM
One thousand Million is also called a Billion. Trillion = Million-Million. = 1012 1 Googol = 10100 1 Googolplex = 10 Googol Natural Numbers
are the class of natural numbers. Now let us understand Prime Triplet, Twin Primes, Co-Prime, perfect Numbers. A number which is divisible by 1 and itself only is called a prime number. The set of three consecutive primes is called Prime Triplet Ex: {3,5,7},{11,13,17}... The prime numbers differing by 2 are called Twin Primes. Ex 3,5 ; 11,13;,... A number for which the sum of all its factors is twice the number is called a Perfect Number (or) the sum of all its factors except itself is the number. Ex: 6,28,496,...etc are Perfect Numbers. Factors of 6 is 1,2,3 and 6. Now 1+2+3=6. more on Perfect
Numbers Properties of Natural Numbers: 1) The general form of an even number is 2n. 2) The general form of an odd number is 2n+1 3) Sum of two even numbers is even. 4) Sum of two odd numbers is even. 5) Sum of an even and an odd number is odd. 6) Square of an odd number is odd. 7) Square of an even number is even. 8) Difference of two odd or two even numbers is always even. 9) Difference of an even number and an odd number is odd. 10) Product of two even is even and two odd is odd. 11) An odd multiplied with an even is even. 12) A square root of an even perfect square is even. 13) A square root of an odd perfect square is odd. 14) Sum of squares of two even is even. 15) Sum of squares of two odd is even. 16) Sum of squares of an even and an odd is odd. 17) The sum of first 'n' odd numbers is n2 18) The sum of first 'n' even numbers is n(n+1) 19) If a natural number "N" is
written as the product of prime factors equal to ap.bq.cr
... then the number of factors of N has is (p+1)(q+1)(r+1)...--------------------------- I invite review and suggestions.
All students can contact me at ganithguru
for further guidance. All about infinity: Non-zero/0 is said to be undefined because division is defined in terms of multiplication. a/b = x is defined to mean that b*x = a. There is no x such that 0*x = 1, since 0*x = 0 for all x. Thus 1/0 does not exist, or is not defined, or is undefined. You wish to introduce a new element (or maybe two elements), infinity, which you wish to append to the real number system. That is not prohibited. After all, that is how we got from natural numbers to integers (appending negative integers and zero), and from integers to rationals (appending ratios of integers), and from rationals to reals (appending limits of convergent sequences), and from reals to complexes (appending the square root of -1). What you end up with is not the real number system, however. Furthermore, if you wish to define the four operations + - * and / for this new system, you probably want them to be the same on real numbers, and just add on the definitions of things like infinity + r and r/infinity, for any real number r. Some of these work fines. It makes sense to define:
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I invite review and suggestions. All students can contact me at ganithguru for further guidance.
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