These

ordinal numbers would need to be handled with the appropriate care:

If it was allowed in the 1950s that a maximum value of an

ordinal number in Periodic Table could not exceed the value Z = 110 due to a spontaneous division of the nucleus, then in the 1960s theoreticians proposed the hypothesis that the atomic nucleus could have anomalously high stability.

Following [1], [4]) The cardinal number of a set A is the initial

ordinal number a in the class of all sets equipotent to A.

1), even repeated in 1990 (Kendall and Gibbons):"we shall often operate with

ordinal numbers as if they were the cardinals of ordinary arithmetic, adding them, subtracting them, and even multiplying them", but he never put this statement into practice at least for subtraction and multiplication.

To determine the

ordinal number of a year on the Jewish calendar given the year of the Gregorian calendar (or vice versa), we can see that such a year is equal to the Gregorian year plus 3760 before 1 Tishri, and the Gregorian year plus 3761 after 1 Tishri.

If a set has a clear order then we need only look for its highest ranked element in order to know its

ordinal number.

In a most attractive article in these pages, Graham Priest (1994) has shown that paradoxes of self-reference in logics and set theory carry a similarity of structure far beyond that which Bertrand Russell had exhibited for his own paradox and those of the greatest cardinal and greatest

ordinal numbers.

So along with the indefinitely extensible concepts of set,

ordinal number, cardinal number, we also get those of natural number and real number.

Contract Awarded for

Ordinal number product name quantity brief technical specifications remark

Then switch to the

ordinal number version of the same song.

In English, we use the combination of the counting number (numerator) and the

ordinal number (denominator) to name, or verbally represent, fractions.

When we describe the child who came in third, we are using an

ordinal number.