- Value Comparisons
Smaller Value/Greater Value < 1
Greater Value/Smaller Value > 1
ax² + bx + c = 0
double bSquared = (b * b);
double twoA = 2 * a;
double calSqrt = Math.sqrt(bSquared - (4 * a * c));
double cal1 = (-b - calSqrt) / twoA;
double cal2 = (-b + calSqrt) / twoA;
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 1, 3, 5, 7, 9, 11, 13 … is an arithmetic progression with common difference 2. If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:
a_n = a_1 + (n - 1) * d
In general
a_n = a_m + (n - m) * d
a_1 = 1
d = 2
For
1, 3, 5, 7, 9, 11, 13…
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54 ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25 ... is a geometric sequence with common ratio 1/2.
Gauss Law
S = Sum of all number's
F = First number in sequence
L = Last number in sequence
T = number of Terms in sequence
S = (F + L) * (T) / 2
double sum = 0.0;
for (int i = 1; i <= N; ++i) {
sum += 1.0 / i;
}
// print out Nth harmonic number
System.out.println(sum);Addition: (x + y) mod n = ((x mod n) + (y mod n)) mod n
Subtraction: (x - y) mod n = ((x mod n) - (y mod n) + n) mod n
Multiplication: (x * y) mod n = ((x mod n) * (y mod n)) mod n
Division: (x / y) mod n = ((x mod n) * (y-1 mod n)) mod n
Power: (a^b) mod n = ((a^(b/2) mod n) * (a^(b/2) mod n)) mod n //assume that b is even
public static double log2(int num) {
return (Math.log10(num) / Math.log10(2));
}
public static double logB(int num, int base) {
return (Math.log10(num) / Math.log10(base));
}
Division:
Dividend ÷ Divisor = Quotient
18 ÷ 3 = 6
Quotient × Divisor = Dividend
6 × 3 = 18
23 ÷ 5 Here Quotient 4 and Remainder 3
Multiplication:
Factor × Factor = Product
3 × 4 = 12
Addition:
Addends/Terms + Addends/Terms = Sum
7 + 7 = 14
Subtraction:
Minuend/Terms – Subtrahend/Terms = Difference
6 – 4 = 2
Numerator/Denominator
Continued Fractions: [CF]
A finite continued fraction is an expression of the form
even ± even = even
even ± odd = odd
odd ± odd = even
odd * odd = odd
even * even = even
even = 2n
odd = 2n + 1
If every element of a set B is also a member of a set A, then we say B is a subset of A. We use the symbol ⊂ to mean “is a subset of” and the symbol ⊄ to mean “is not a subset of”.
Example:
A = {1, 3, 5}, B = {1, 2, 3, 4, 5}
So, A ⊂ B because every element in A is also in B.
X = {1, 3, 5}, Y = {2, 3, 4, 5, 6}.
X ⊄ Y , because 1 is in X but not in Y.
• Every set is a subset of itself i.e. for any set A, A ⊂ A
• The empty set is a subset of any set A i.e. Ø ⊂ A
• For any two sets A and B, if A ⊂ B and B ⊂ A then A = B
The number of subsets for a finite set A is given by the formula: Number of subsets = 2 n (A), where n (A) = number of elements in the finite set A List all the subsets of the set Q = {x, y, z}. The subsets of Q are
{ }, {x}, {y}, {z}, {x, y}, {x, z}, {y, z} and {x, y, z}
N (Q) = 3
Number of subsets = 23 = 8
Something/0 = undefined (অসংজ্ঞায়িত)
// it has two limiting value -∝ and +∝
// if we know the value is positive then we can put +∝
// mass = 97/0, mass cannot be negative so we can write mass = +∝
0/0 = indeterminate (অনিণেয়)