Commonly used measures of population aging categorize adults into those who are "old" and those who are not. How this threshold of the stage of "old age" is determined is crucial for our understanding of population aging. We propose that the old age threshold be determined using an equivalency criterion. People at the old age threshold should be roughly equivalent to one another in relevant characteristics regardless of when and where they lived. The UN publishes two variants of the potential support ratio based on different old age thresholds. One old age threshold is based on a fixed chronological age and the other on a fixed remaining life expectancy. Using historical data on 5-year death rates at the old age threshold as an indicator of one aspect of health, we assess the extent to which the two approaches are consistent with the equivalency criterion. The death rates are derived from all the complete cohort life tables in the Human Mortality Database. We show that the old age threshold based on a fixed remaining life expectancy is consistent with the equivalency criterion, while the old age threshold based on a fixed chronological age is not. The picture of population aging that emerges when measures consistent with the equivalency criterion are used are markedly different from those that result when the equivalency criterion is violated. We recommend that measures of aging that violate the equivalency criterion should only be used in special circumstances where that violation is unimportant.