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)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Alephs of Sums@infinity

**Physics Forums | Science Articles, Homework Help, Discussion**