in mathematics, we lose concept of how many and fall back to cardinality, which has a lose correlation with how many. So asking &quot;are there the same number&quot; of integers as rational numbers gets a little iffy until we make some definitions. We just say that we can create a bijection from integers to rationals. They each index the other, and for each thing in one, there is one and only one thing in the other. Does this mean there are the same &quot;many&quot;? Well loosely, and in the context of cardinality, yes. But things get weird because there are the same &quot;many&quot; of the whole as a subset (ie, there are as &quot;many&quot; even numbers as integers, as &quot;many&quot; positive numbers as positive and negative integers, etc).<p>But most people would disagree with you when you say &quot;how can there be more rational numbers than integers...&quot; because while we don&#x27;t have a firm grasp of how many, we definitely would say that having the same cardinality means that there isn&#x27;t some notion of &quot;more&quot;.<p>I&#x27;m not sure what you mean by mathematical operations or concepts that depend on this.