What is the similarity between cardinal utility theory and ordinal utility theory?

When discussing cardinal vs. ordinal, it is helpful to look at what the Words mean. The distinguishing factor here is between cardinal and ordinal numbers. Cardinal numbers are 1, 2, 3; ordinal numbers, 1st, 2nd, 3rd. Some crucial differences follow from that. Whereas mathematical operations can be performed on cardinal numbers, they cannot be performed on ordinal numbers. Now, when talking about cardinal utility, it is an attempt to ''measure the utility of various alternatives. When talking about ordinal utility, it is the ''ranking of alternatives.'''' Cardinal utility is, however, an erroneous concept. It is impossible to "measure" utility. People can only say "I prefer A to B", but cannot meaningfully say "I prefer A 2.5 times more than B" or something to that effect. Furthermore, comparisons of utility between different individuals are impossible and meaningless, as well as between the same individual at different points in time (as individuals can and do change their preferences -- that is, ordinal value-scale rankings). Because value is subjective, we cannot measure it and cannot compare between two different people, or even between the same person at different times. To clarify, ordinal utility culminates in value-scales: 1st: A

2nd: B

3rd: C whereas cardinal utility is the erroneous attempt at measurement: 10utils -- A

7utils -- B

3utils -- C

Omar Tawfik.