The natural number 5 as a set

For natural numbers, the Von Neumann definition is usually used: A natural number N then is the set of all lower natural numbers, with 0 being the empty set.

N1 < N2 is defined as N1 ∈ N2.

N + 1 is defined as N ∪ { N }.

N + 0 is defined as N.

N1 + (N2 + 1) is defined as (N1 + N2) + 1.

5 = { 0 , 1 , 2 , 3 , 4 }

5 is the 66185228434044942951864067458396061614989522267577311297802947435570493724401440549267868490798926773634494383968047143923956857140205406402740536087446083831052036848232439995904404992798007514718326043410570379830870463780085260619444417205199197123751210704970352727833755425876102776028267313405809429548880554782040765277562828362884238325465448520348307574943345990309941642666926723379729598185834735054732500415409883868361423159913770812218772711901772249553153402287759789517121744336755350465901655205184917370974202405586941211065395540765567663193297173367254230313612244182941999500402388195450053080385548th set in Vω

See also 5 in Linked Open Numbers

(back to √2)