Math 295. Handout on Shorthand The phrases \u201cfor all\u201d, \u201cthere exists\u201d, and \u201csuch that\u201d are used so frequently in mathematics that we have found it useful to adopt the following shorthand. The symbol \u2200 means \u201cfor all\u201d or \u201cfor any\u201d. The symbol \u2203 means \u201cthere exists\u201d.