ordinals's Usage Examples:

The definitions of the finite ordinals can be expressed without use of the corresponding cardinals, so there is no essential priority of cardinals to ordinals.

Similarly, a class of serial relations, called well-ordered serial relations, can be defined, such that their corresponding relation-numbers include the ordinary finite ordinals, but also include relation-numbers which have many properties like those of the finite ordinals, though the fields of the relations belonging to them are not finite.

are used sometimes as ordinals, i.

Williams: " Proof theoretic ordinals and hierarchies " .

In the case of lists and schedules the numbers are only ordinals; but in the case of mathematical or statistical tables they are usually regarded as cardinals,though, when they represent values of a continuous quantity, they must be regarded as ordinals (§§ 26, 93).

transfinite ordinals is one of the things to be explained.

larger ordinals correspond to more sophisticate descriptions of arithmetic.

Thus (writing ordinals in light type, and cardinals in heavy type) 9 comes after 4, and therefore 9 is greater than 4.

It will suffice to mention here that Peano's fourth premiss of arithmetic does not hold for infinite cardinals or for infinite ordinals.

"This is almost always true of proofs that use countable ordinals.

clock-faces, milestones and chemists' prescriptions), they are still used for ordinals.

Now comes the moment to admit that my ` applications ' of countable ordinals were, in a sense, a con.

This is almost always true of proofs that use countable ordinals.

Synonyms:

155th, 125th, 140th, forty-seventh, 150th, 11th, 105th, thirty-eighth, 9th, hundred-and-twentieth, two-hundredth, centesimal, 75th, ninety-fifth, eighteenth, twenty-sixth, thirty-fourth, 180th, fifth, 2d, hundred-and-forty-fifth, 50th, ninetieth, 90th, 55th, 80th, three-hundredth, twenty-third, 14th, forty-first, 37th, 27th, 40th, 3rd, four-hundredth, hundred-and-fortieth, fortieth, 190th, 100th, thirty-sixth, eleventh, seventy-fifth, forty-sixth, forty-fourth, hundred-and-seventy-fifth, forty-eighth, thirty-ninth, hundred-and-tenth, quaternary, 24th, 47th, twenty-fifth, fiftieth, 29th, 145th, tertiary, thirty-second, 115th, n-th, 175th, hundred-and-fiftieth, hundred-and-fifth, 41st, 64th, quintillionth, 34th, 120th, 95th, hundred-and-thirty-fifth, 300th, thirty-third, 38th, 42nd, 23rd, 26th, 6th, 48th, ninth, hundred-and-sixty-fifth, 16th, fourth, 110th, hundredth, 170th, hundred-and-fifteenth, thirty-seventh, 1000th, seventh, 33rd, 35th, first, sixty-fifth, umptieth, thirtieth, forty-third, twelfth, sixteenth, eightieth, 25th, twenty-fourth, nineteenth, 1st, 17th, fifteenth, sixth, 32nd, seventeenth, millionth, umteenth, 13th, tenth, hundred-and-first, fourteenth, sixty-fourth, 12th, thirty-first, twentieth, 28th, hundred-and-seventieth, thirteenth, 46th, 500th, 20th, 101st, seventieth, eighty-fifth, 130th, 2nd, twenty-second, zero, forty-second, 65th, 70th, twenty-first, 22nd, 5th, thousandth, 45th, 18th, hundred-and-thirtieth, 36th, 200th, hundred-and-sixtieth, 10th, zeroth, 19th, hundred-and-fifty-fifth, billionth, sixtieth, twenty-ninth, fifty-fifth, 400th, 165th, forty-fifth, 39th, twenty-seventh, 160th, five-hundredth, eighth, 21st, 30th, third, hundred-and-twenty-fifth, hundred-and-ninetieth, trillionth, 31st, second, 44th, hundred-and-eightieth, 4th, twenty-eighth, forty-ninth, 8th, thirty-fifth, umpteenth, 49th, 43rd, 85th, 15th, 7th, nth, 135th, 60th, quadrillionth,

Antonyms:

all, some, former, disagreement, cardinal,