Select the first number of a list that is lower than a given number

Question

If I have a list such as:

list={40,40.,40.,40.,40.0001,40.0001,40.0001,40.0002,40.0002,40.0003,40.0003,40.0004,40.0005,40.0005,40.0006,40.0007,40.0008,40.0009,40.001,40.0011,40.0013,40.0014,40.0015,40.0017,40.0018,40.002,40.0021,40.0023,40.0024,40.0026,40.0028,40.003,40.0032,40.0034,40.0036,40.0038,40.004,40.0042,40.0044,40.0047,40.0049,40.0052,40.0054,40.0057,40.0059,40.0062,40.0065,40.0068,40.0071,40.0074,40.0077,40.008,40.0083,40.0086,40.0089,40.0092,40.0096,40.0099,40.0103,40.0106,40.011,40.0113,40.0117,40.0121,40.0125,40.0129,40.0133,40.0137,40.0141,40.0145,40.0149,40.0153,40.0158,40.0162,40.0167,40.0171,40.0176,40.018,40.0185,40.019,40.0194,40.0199,40.0204,40.0209,40.0214,40.0219,40.0224,40.023,40.0235,40.024,40.0246,40.0251,40.0257,40.0262,40.0268,40.0274,40.0279,40.0285,40.0291,40.0297,40.0303,40.0309,40.0315,40.0321,40.0328,40.0334,40.034,40.0347,40.0353,40.036,40.0366,40.0373,40.038,40.0386,40.0393,40.04,40.0407,40.0414,40.0421,40.0428,40.0436,40.0443,40.045,40.0458,40.0465,40.0473,40.048,40.0488,40.0495,40.0503,40.0511,40.0519,40.0527,40.0535,40.0543,40.0551,40.0559,40.0567,40.0575,40.0584,40.0592,40.0601,40.0609,40.0618,40.0626,40.0635,40.0644,40.0653,40.0662,40.0671,40.068,40.0689,40.0698,40.0707,40.0716,40.0725,40.0735,40.0744,40.0754,40.0763,40.0773,40.0782,40.0792,40.0802,40.0812,40.0822,40.0832,40.0842,40.0852,40.0862,40.0872,40.0882,40.0893,40.0903,40.0914,40.0924,40.0935,40.0945,40.0956,40.0967,40.0977,40.0988,40.0999,40.101,40.1021,40.1032,40.1043,40.1055,40.1066,40.1077,40.1089,40.11,40.1112,40.1123,40.1135,40.1147,40.1158,40.117,40.1182,40.1194,40.1206,40.1218,40.123,40.1242,40.1255,40.1267,40.1279,40.1292,40.1304,40.1317,40.1329,40.1342,40.1355,40.1367,40.138,40.1393,40.1406,40.1419,40.1432,40.1445,40.1459,40.1472,40.1485,40.1499,40.1512,40.1526,40.1539,40.1553,40.1566,40.158,40.1594,40.1608,40.1622,40.1636,40.165,40.1664,40.1678,40.1692,40.1706,40.1721,40.1735,40.175,40.1764,40.1779,40.1793,40.1808,40.1823,40.1838,40.1853,40.1868,40.1883,40.1898,40.1913,40.1928,40.1943,40.1958,40.1974,40.1989,40.2005,40.202,40.2036,40.2051,40.2067,40.2083,40.2099,40.2115,40.2131,40.2147,40.2163,40.2179,40.2195,40.2211,40.2228,40.2244,40.2261,40.2277,40.2294,40.231,40.2327,40.2344,40.236,40.2377,40.2394,40.2411,40.2428,40.2445,40.2462,40.248,40.2497,40.2514,40.2532,40.2549,40.2567,40.2584,40.2602,40.262,40.2637,40.2655,40.2673,40.2691,40.2709,40.2727,40.2745,40.2763,40.2782,40.28,40.2818,40.2837,40.2855,40.2874,40.2892,40.2911,40.293,40.2948,40.2967,40.2986,40.3005,40.3024,40.3043,40.3062,40.3082,40.3101,40.312,40.314,40.3159,40.3179,40.3198,40.3218,40.3237,40.3257,40.3277,40.3297,40.3317,40.3337,40.3357,40.3377,40.3397,40.3417,40.3437,40.3458,40.3478,40.3499,40.3519,40.354,40.356,40.3581,40.3602,40.3623,40.3644,40.3664,40.3685,40.3707,40.3728,40.3749,40.377,40.3791,40.3813,40.3834,40.3856,40.3877,40.3899,40.392,40.3942,40.3964,40.3986,40.4008,40.403,40.4052,40.4074,40.4096,40.4118,40.414,40.4163,40.4185,40.4208,40.423,40.4253,40.4275,40.4298,40.4321,40.4343,40.4366,40.4389,40.4412,40.4435,40.4458,40.4481,40.4505,40.4528,40.4551,40.4575,40.4598,40.4622,40.4645,40.4669,40.4693,40.4716,40.474,40.4764,40.4788,40.4812,40.4836,40.486,40.4884,40.4909,40.4933,40.4957,40.4982,40.5006,40.5031,40.5055,40.508,40.5105,40.5129,40.5154,40.5179,40.5204,40.5229,40.5254,40.5279,40.5305,40.533,40.5355,40.5381,40.5406,40.5431,40.5457,40.5483,40.5508,40.5534,40.556,40.5586,40.5612,40.5638,40.5664,40.569,40.5716,40.5742,40.5768,40.5795,40.5821,40.5848,40.5874,40.5901,40.5927,40.5954,40.5981,40.6008,40.6035,40.6062,40.6089,40.6116,40.6143,40.617,40.6197,40.6224,40.6252,40.6279,40.6307,40.6334,40.6362,40.6389,40.6417,40.6445,40.6473,40.6501,40.6529,40.6557,40.6585,40.6613,40.6641,40.6669,40.6698,40.6726,40.6755,40.6783,40.6812,40.684,40.6869,40.6898,40.6926,40.6955,40.6984,40.7013,40.7042,40.7071,40.71,40.713,40.7159,40.7188,40.7218,40.7247,40.7277,40.7306,40.7336,40.7366,40.7395,40.7425,40.7455,40.7485,40.7515,40.7545,40.7575,40.7605,40.7636,40.7666,40.7696,40.7727,40.7757,40.7788,40.7818,40.7849,40.788,40.791,40.7941,40.7972,40.8003,40.8034,40.8065,40.8096,40.8128,40.8159,40.819,40.8222,40.8253,40.8285,40.8316,40.8348,40.8379,40.8411,40.8443,40.8475,40.8507,40.8539,40.8571,40.8603,40.8635,40.8667,40.8699,40.8732,40.8764,40.8797,40.8829,40.8862,40.8894,40.8927,40.896,40.8993,40.9026,40.9059,40.9092,40.9125,40.9158,40.9191,40.9224,40.9257,40.9291,40.9324,40.9358,40.9391,40.9425,40.9458,40.9492,40.9526,40.956,40.9594,40.9628,40.9662,40.9696,40.973,40.9764,40.9798,40.9833,40.9867,40.9902,40.9936,40.9971,41.0005,41.004,41.0075,41.0109,41.0144,41.0179,41.0214,41.0249,41.0284,41.0319,41.0355,41.039,41.0425,41.0461,41.0496,41.0532,41.0567,41.0603,41.0639,41.0674,41.071,41.0746,41.0782,41.0818,41.0854,41.089,41.0926,41.0963,41.0999,41.1035,41.1072,41.1108,41.1145,41.1181,41.1218,41.1255,41.1291,41.1328,41.1365,41.1402,41.1439,41.1476,41.1513,41.1551,41.1588,41.1625,41.1663,41.17,41.1738,41.1775,41.1813,41.185,41.1888,41.1926,41.1964,41.2002,41.204,41.2078,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99,50.8814,50.8928,50.9042,50.9157,50.9271,50.9386,50.95,50.9615,50.973,50.9844,50.9959,51.0074,51.0189,51.0304,51.0419,51.0534,51.065,51.0765,51.088,51.0996,51.1111,51.1227,51.1342,51.1458,51.1573,51.1689,51.1805,51.1921,51.2037,51.2153,51.2269,51.2385,51.2501,51.2617,51.2733,51.285,51.2966,51.3083,51.3199,51.3316,51.3432,51.3549}

How can I find the first value of the list that is immediately below and closest to 50 (in this case it would be 49.9974?. I tried using closest = SelectFirst[list, # < 50 &] but it seems this does not work with list with numbers in ascending order. I do not want to use Nearest[list, 50] because I also have other list where the closest number to 50 may be the a higher number than 50 (e.g. 50.0001) and I am only interested in the closest number to 50 that is immediately lower than 50 in a list of ascending order.

Thank you!

Answer 1

Okay, so, let's see why SelectFirst worked for the greater-than case, and why Max is a better option for the less-than case, especially if we have an unordered list as our input:

lthan = Select[list, # < 50 &];
gthan = Select[list, # > 50 &];
#@lthan & /@ {Max, First, Last}
#@gthan & /@ {Min, First, Last}

(* {49.9974, 40, 49.9974} *)
(* {50.0083, 50.0083, 51.3549} *)

However, the above may not be explanative enough, so, if we wanted to use SelectFirst the list should be ordered in such a way as to allow for this. In your previous question, it was strictly descending, and so we can see the same thing here:

SelectFirst[Reverse@list, # < 50 &]

(* 49.9974 *)

And, the following might be interesting or useful to you:

MinMax /@ GatherBy[list, # < 50 &]

(* {{40, 49.9974}, {50.0083, 51.3549}} *)

Finally, using something like Position, Sort, or Ordering, we could also make an attempt at this procedure for an unordered list...but that is outside of the scope of this QA.