How do I represent the quantity of terms for a summation with an upper limit approaching infinity? In the attached image, the limit is obviously infinity, but the quantity of terms(adsbygoogle = window.adsbygoogle || []).push({}); followingthe summation is countable! (as the upper limit approaches infinity, the quanitity of terms approaches a countable infinity (natural numbers)). If x can be reals, then the expression would not work, as reals would cause an uncountable infinity. However, x can be either rational or irrational, but i have a problem when i set the domain to BOTH rational and irrational at the same time in the same domain. It seems that x can be either, but not both at the same time.(see the uploading image)

Well, i'm just wondering, but what is really the domain of the expression---what set of numbers does x belong to?? In addition, how could i represent the quantity of terms following the sigma sum; what aleph would i use? In addition, how would i write the upper limit as acountableinfinity? (not with a sideway eight, cuz i want to show that it approaches a countable infinity. Maybe the aleph-upsilon, or just the upsilon symbol would do?)

*this seems a simple problem for which i couldn't solve for some reason//maybe lack of knowledge of something....worse.. However, i seemed to have chosen this problem to present to my class (i'm a high-school junior, but this was just a small extra-credit problem), so i researched some material over the internet. unfortunately, it wasn't enough and the info seemed too vague)

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# Alephs of Sums@infinity

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