Assuming an endless universe, there are as many Thursdays as there are days.

Indeed, I am attempting to apply fractions to infinite values, "in error." In error when we're talking about real numbers. However, infinity does not exist in the real numbers, and so it is clear that real numbers are not fit for our purposes, since we are talking about infinite values. Indeed, in the real numbers, adding a number to infinity does nothing. Take something we know, for example. We know that whole numbers, all integers and zero, contains exactly one more member than the natural numbers. However, since infinite is only a concept rather than a set of well-defined values in the real numbers, these sets have the same cardinality. That is to say, by my opponent's reasoning, they contain exactly the same number of members, even though we know that one of the sets is the exact same as the other set except with one more member. Indeed, the problem is rooted in the real number system as it pertains to infinite values. Even multiplying an infinite value by a scalar does not affect the value in the real number system. Since infinity is not a set of well-defined values in the real number system, we should seek another system where it is a meaningful concept, since our specific problem is dealing with the values of infinite numbers, which are not well defined in the reals. Let me be clear on something. Even though [in the reals] adding 1 to an infinite value doesn't change the infinite value, two infinite sets with a difference in members of one still has a different number of members. There is a reason Infinity - Infinity does not equal 0 - because even though we cannot make the difference between the two infinities clear, there may still be some difference. Indeed, Infinity/Infinity may not always be 1. In the case we are given, the ratio of the infinities is one-to-seven, meaning that each Thursday brings with it 7 days. Simply because we cannot differentiate these values in their infinite form does not mean that they are equal. If they were equal, Infinity/Infinity would indeed be 1, and Infinity - Infinity would be zero. So if we simply pretend that infinite numbers exist, and we graph the function I gave last round at some infinite value [meaning that some infinite number of days has passed], then we see that seven times as many days exist as Thursdays. The function indeed reduced itself to f(x)=1/7, meaning that the value is constant everywhere it is valid. And since we are now using a number system where infinite is valid, we see that it continues to be 1/7 at that point. For something to be equivalent [like the number of days and the number of Thursdays], there must be a difference of zero between them. However, it cannot be said that the difference between these two functions is ever zero, let alone at infinity. Indeed, the difference between the two functions, x and x/7, GROWS as we get to larger and larger numbers. At infinity, the difference between the two is infinite. And while that may not mean anything mathematically in the real numbers, it surely means something semantically in reference to this very discussion. The fact that there is any difference means we can negate. I apologize for so readily accepting the idea that the number of whole numbers and their squares is equivalent, since that only holds true mathematically using number systems with poorly-defined concepts of infinity. In the reals, if we define X as some infinite value, X + 1 equals X. We find that 7X = X. Thus, there can be any finite difference in the size of the two sets, or one set could be seven times as large as the other, yet my opponent would argue that since the real number system is so inept at handling infinite numbers, the two sets have the same number of members. Indeed, my opponent argues that 1/7 of infinity is infinity. This is true mathematically using reals, but we must also realize that one set has seven times as many members, since we are actively incrementing in days. At any time T, seven times as many days have passed as Thursdays. Thus, there are not 'as many' Thursdays as there are days. This will hold true at the end of every Thursday, even Thursdays of infinitely-numbered weeks.