less duplicvation and high co-ordinality in b-tree where as more duplication and less co-ordinality in mbitmap

The answer depends on what the ordinality is based on:

distance from the sun/orbital period

distance from the earth

brightness in our night sky

size/mass

number of moons

when discovered

when visited (fly past) by a spacecraft

Each one of these will probably generate a different ordinal number.

The history of economic thought remembers António Horta Osório for Schumpeter's reference to him in the History of Economic Analysis, in the context of a general appraisal of available works using mathematical instruments and language. This, however, does not do him justice, as he should also be praised for his pioneering interpretation of Pareto's general equilibrium. According to Stigler (1965), the definitive substitution of the cardinal utility hypothesis for the ordinal utility perspective was achieved by Johnson (1913) and Slutsky (1915). Weber (2001) discusses how far Pareto used cardinality, elects Slutsky (1915) as a pioneer of demand theory and prefers to reserve to R. G. Allen (1932-34), L. R. Klein and H. Rubin (1947-48), Samuelson (1947-48), R. C. Geary (1950-51), and Richard Stone (1954) the role of establishing ordinal utility in studying the utility function. This paper shows that Osório (1911) considered the subject of ordinalism before Johnson and Slutsky addressed the issue, as he had rejected the possibility of measuring utility and clearly stated that general equilibrium is not affected if cardinality is replaced by the ordinal conception for utility, according to Pareto's last formulation. Upon reading his book it becomes clear that not only was he perfectly aware of Edgeworth's contribution on the utility indifference curves, but also of Pareto's attempts to preserve general equilibrium from Fisher's criticism against cardinalism. Historians of economic thought have forgotten one of the early twentieth-century neoclassical economists. In this way the History of Economics has neglected an interesting proof of the consolidation of the Paretian ideas on ordinality, an issue that was an exciting and uncharted territory at that moment.

To list a few:

A

absolute value. addends. additive identity. additive inverse. algorithm. angle. approximate number. arithmetic number. associative property. axioms. addition. abscissa. adjacent. array. arc. area. accuracy of. acute triangle.

B

base. binary operation. binary numeration system. binary. bit. byte.

C

circle. circumference. closed curve. closure. common factor of two numbers. commutative

property. complete factorization of a natural number. composite number. constant. counting numbers. curve. congruent triangle. complementary. cardinal number. center. cone. congruence. coordinates. correspondence. cube. cylinder. cardinality.

D

decimal fractions. decimal numerals. denominator. diameter. digit symbols. distribute property. dividend. divisibility. divisor. duodecimal system. division. decimal point. degree. digits. disjoint sets. deviation. diagonal.

E

empty set. endpoint. equal sets. equation. equilateral triangle. equivalent sentences. equivalent sets. even number. exponent. equal. element. error of measurement. event space. error of. Egyptian numerals. expanded numerals.

F

factor of a product. factor of a number. factor as verb. finite sets. fraction. fractional number. factoring. face. frequency distribution. figure.

G

geometric figure. geometry. greatest common factor of several numbers. graph. greater than. greatest possible error.

H

hexadecimal. horizontal. half plane. histogram. Hindu-Arabic numerals. hypotenuse.

I

identity for an operation. infinite set. integers. intersection of several sets. inverse elements. inverse operations. irrational number. isosceles triangle. isosceles right. inequalities. intersection of.

J

juxtapose

K-

L

line segment. least common multiple of several numbers. length. lateral edges. lateral faces. lateral surfaces. least common denominator. legs. less than. line.

M

measure. minuend. modular arithmetic. modulus. multiples of a number. multiplication. mean. median. mode. measurement. metric system.

N

natural numbers. null set. number line. numeral. numerator. numerical coefficient. number bases. numbers. numeration systems. negative.

O

odd number. one-to-one correspondence. open sentence. operation. opposite operations. ordinal number. ordinality. order. ordered pair. ordinate. origin. obtuse triangle. octal.

P

place value. percent. perimeter. plane. point. polygon. precision of. prime factorization.

prime number. proper subset. proportion. parallel lines. perpendicular lines. probability.

parallelogram. polygon. polynomial. percentage. place of positional values. placeholder. prism. pyramid. Phytagorean Theorem. protractor. product. positive.

q-

quadrilateral family.

R

radical. ratio. rational numbers. ray. real numbers. repeating decimal numeral. reciprocal. rectangle. rhombus. radius. relative error. renaming a number. rounded number. roman numeral. replacement set. right triangle.

S

scientific notation. segment. set. simple closed curve. solution set. space. square. square root of a number. subset. subtraction. symbol. supplementary. semicircle. skew lines. standard deviation. surface area. sentences. sphere. scalene. similar. sides. sum.

T

terminating decimals. trapezoid. triangle. transversal. truth set. transpose.

U

universal set. uniqueness. units of weight. units of length. units of capacity. union of.

V

vertex angles. vertical. variable. volume. vertices.

W

whole numbers. well-defined set.

X

x-axis. x (as literal that represents the unknown).

Y

y-axis.

Z

zero.

addition binomial counting decimal estimate fractions graphs horizontal irrational j k line multiply numbers octagon product questions rational subtract t u variable w x y z