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.mw-parser-output .nota-disambigua{clear:both;margin-bottom:.5em;border:1px solid #CCC;padding-left:4px}.mw-parser-output .nota-disambigua i{vertical-align:middle} Disambiguazione – Se stai cercando altri significati, vedi Ripa (disambigua) . R. XII Ripa Piazza Bocca della Verità Stato   Italia Regione   Lazio Provincia   Roma Città Roma Capitale Circoscrizione Municipio Roma I Codice 112 Superficie 0,8485 km² Abitanti 2 520 ab. [1] (2016) Densità 2 969,95 ab./km² Coordinate: 41°53′07.25″N 12°28′54.48″E  /  41.885346°N 12.481799°E 41.885346; 12.481799 Ripa è il dodicesimo rione di Roma, indicato con R. XII . Appartiene al rione Ripa anche l'Isola Tiberina. Indice 1 Geografia fisica 1.1 Territorio 2 Storia 2.1 Porto di Ripa Grande 2.2 Stemma 3 Monumenti e luoghi d'interesse 3.1 Architetture civili 3.2 Architetture religiose 3.3 Architetture militari 3.4 Alt...

1 $begingroup$ I was given the following function: $$ f(x) = begin{cases} frac{1}{q} &text{if }x = frac{p}{q} text{ is rational, reduced to lowest terms} \ 0 &text{if }x text{ is irrational}end{cases}$$ And was asked to attempt to prove or disprove whether or not, for some $j$ on the interval $(0,1)$ , $lim limits_{x to j}{}f(x)$ exists. Intuitively, I know that I can find an irrational number between any two rationals which would obviously result in some discontinuity. I considered the idea that maybe it could be possible assuming that among the infinitely many rationals on the interval which also share a common denominator and could be used to find the limit, but that obviously would not work. However, I cannot formulate any proper line of reason to prove the limit does not exist. How can I prove t...