Using solely the operations +, -, flooring, ceiling, factorial (Gamma operate extension), and sq. root:

1 = 2 – 0! + 0 + 0

2 = 2 + 0 + 0 + 0

3 = 2 + 0! + 0 + 0

4 = 2 + 0! + 0! + 0

5 = (2 + 0!)! – 0! + 0

6 = (2 + 0!)! + 0 + 0

7 = (2 + 0!)! + 0! + 0

8 = (2 + 0!)! + 0! + 0!

9 = ceil((sqrt(2)! + 0! + 0!)!) + 0

10 = flooring((sqrt(2) + 0! + 0!)!) + 0

11 = ceil((sqrt(2) + 0! + 0!)!) + 0

12 = ceil((sqrt(2) + 0! + 0!)!) + 0!

13 = ceil((sqrt(2)! + 0!)!!!) + 0 + 0

14 = flooring((sqrt((2 + 0!)! + 0!) + 0!)!)

15 = ceil((sqrt((2 + 0!)! + 0!) + 0!)!)

16 = flooring((sqrt(2 + 0!) + 0! + 0!)!)

17 = ceil((sqrt(2 + 0!) + 0! + 0!)!)

18 = ceil((sqrt(2)!! + 0!)!!!!) + 0 + 0

19 = ceil((sqrt(sqrt((2 + 0!)! + 0!)) + 0!)!!)

20 = flooring((sqrt((2 + 0! + 0!)!) – 0!)!)

21 = flooring(sqrt((2 + 0!)! + 0!)!!) + 0

22 = ceil((sqrt(2) + 0!)!)! – 0! – 0!

23 = (2 + 0! + 0!)! – 0!

24 = (2 + 0! + 0!)! + 0

25 = (2 + 0! + 0!)! + 0!

26 = flooring(sqrt((2 + 0!)!!)) + 0 + 0

27 = ceil(sqrt((2 + 0!)!!)) + 0 + 0

28 = ceil(sqrt((2 + 0!)!!)) + 0! + 0

29 = ceil(sqrt((2 + 0!)!!)) + 0! + 0!

30 = ceil((sqrt((2 + 0!)!)! + 0!)!) + 0

31 = flooring(sqrt((sqrt(2) + 0!)!!!)) – 0! + 0

32 = flooring((sqrt(sqrt(2)) + 0! + 0! + 0!)!)

33 = ceil((sqrt(sqrt(2)) + 0! + 0! + 0!)!)

34 = ceil(sqrt((sqrt(2) + 0!)!!!)) + 0! + 0

35 = flooring((sqrt(2)! + 0! + 0! + 0!)!)

36 = ceil((sqrt(2)! + 0! + 0! + 0!)!)

37 = ceil(((sqrt(2)!! + 0!)! + 0! + 0!)!)

38 = flooring((sqrt(2 + 0!) + 0!)!!) – 0!

39 = flooring((sqrt(2 + 0!) + 0!)!!) + 0

40 = ceil((sqrt(2 + 0!) + 0!)!!) + 0

41 = ceil((sqrt(2 + 0!) + 0!)!!) + 0!

42 = flooring((sqrt((sqrt(2) + 0!)!) + 0!)!!) + 0

43 = ceil((sqrt((sqrt(2) + 0!)!) + 0!)!!) + 0

44 = flooring(((sqrt(sqrt(2)) + 0!)! + 0! + 0!)!)

45 = flooring((sqrt(2) + 0! + 0! + 0!)!)

46 = ceil((sqrt(2) + 0! + 0! + 0!)!)

47 = ceil(sqrt(sqrt(((sqrt(sqrt(2)) + 0!)! + 0!)!!))) + 0

48 = flooring((sqrt((2 + 0!)!) + 0! + 0!)!)

49 = ceil((sqrt((2 + 0!)!) + 0! + 0!)!)

50 = ceil(sqrt(((sqrt(sqrt(2)) + 0! + 0!)! – 0!)!))

51 = flooring((sqrt((sqrt(2) + 0!)!!) + 0! + 0!)!)

52 = flooring(sqrt((sqrt(sqrt(2)) + 0! + 0!)!)!!) + 0

53 = flooring(sqrt(sqrt((sqrt(2) + 0! + 0!)!!))) + 0

54 = flooring(((sqrt(sqrt(2) + 0!) + 0!)! + 0!)!)

55 = ceil(((sqrt(sqrt(2) + 0!) + 0!)! + 0!)!)

56 = flooring(((sqrt(2)! + 0!)!! + 0!)!) + 0

57 = ceil(((sqrt(2)! + 0!)!! + 0!)!) + 0

58 = ceil(((sqrt(2)! + 0!)! + 0! + 0!)!)

59 = ceil(((sqrt(sqrt((2 + 0!)!)) + 0!)! + 0!)!)

60 = ceil(sqrt(flooring(sqrt((2 + 0!)! + 0!)!!))!) + 0

61 = flooring(sqrt(sqrt((2 + 0!)! + 0!)!!)!) + 0

62 = ceil(sqrt(sqrt((2 + 0!)! + 0!)!!)!) + 0

63 = flooring((sqrt(sqrt(sqrt(2)) + 0! + 0!) + 0!)!!)

64 = ceil((sqrt(sqrt(sqrt(2)) + 0! + 0!) + 0!)!!)

65 = ceil(sqrt((sqrt((sqrt(2) + 0! + 0!)!)! – 0!)!))

66 = flooring((sqrt(ceil((sqrt(2) + 0!)!!)) + 0! + 0!)!)

67 = flooring(((sqrt(2 + 0!)! + 0!)! + 0!)!)

68 = ceil(((sqrt(2 + 0!)! + 0!)! + 0!)!)

69 = flooring(sqrt(((2 + 0!)! + 0!)!)) – 0!

70 = flooring(sqrt(((2 + 0!)! + 0!)!)) + 0

71 = ceil(sqrt(((2 + 0!)! + 0!)!)) + 0

72 = ceil(sqrt(((2 + 0!)! + 0!)!)) + 0!

73 = flooring((sqrt(sqrt(sqrt(2) – 0!)) + 0! + 0!)!!)

74 = flooring((sqrt(sqrt(2)! + 0! + 0!) + 0!)!!)

75 = ceil((sqrt(sqrt(2)! + 0! + 0!) + 0!)!!)

76 = ceil((((sqrt(2) – 0!)! + 0!)! + 0!)!!)

77 = flooring(sqrt(sqrt(sqrt(((2 + 0!)! – 0!)!)!))) + 0

78 = ceil(sqrt(sqrt(sqrt(((2 + 0!)! – 0!)!)!))) + 0

79 = flooring(sqrt(sqrt(ceil((sqrt(2) + 0! + 0!)!)!))) + 0

80 = ceil(sqrt(sqrt(ceil((sqrt(2) + 0! + 0!)!)!))) + 0

81 = flooring(sqrt((sqrt(2)!! + 0! + 0!)!!)) + 0

82 = ceil(sqrt((sqrt(2)!! + 0! + 0!)!!)) + 0

83 = ceil(((sqrt(2)!! + 0!)!!! + 0!)!) + 0

84 = flooring(sqrt(ceil((sqrt(2) + 0!)!)! – 0!)!) – 0!

85 = flooring(sqrt((2 + 0! + 0!)! – 0!)!)

86 = ceil(sqrt((2 + 0! + 0!)! – 0!)!)

87 = flooring(sqrt(((sqrt(2) + 0!)!! + 0!)!)) + 0

88 = ceil(sqrt(((sqrt(2) + 0!)!! + 0!)!)) + 0

89 = ceil(sqrt(sqrt((2 + 0!)!)!!!)) + 0 + 0

90 = ceil(sqrt(sqrt((2 + 0!)!)!!!)) + 0! + 0

91 = ceil(sqrt(sqrt((2 + 0!)!)!!!)) + 0! + 0!

92 = flooring(((sqrt(sqrt(2) – 0!)! + 0!)! + 0!)!!)

93 = ceil(((sqrt(sqrt(2) – 0!)! + 0!)! + 0!)!!)

94 = flooring(sqrt((2 + 0!)! + 0! + 0!)!!)

95 = ceil(sqrt((2 + 0!)! + 0! + 0!)!!)

96 = ceil(sqrt(flooring((sqrt(2)! + 0! + 0!)!))!!) + 0!

97 = flooring(sqrt(sqrt(((sqrt(2) + 0! + 0!)! + 0!)!)))

98 = ceil(sqrt(sqrt(((sqrt(2) + 0! + 0!)! + 0!)!)))

99 = flooring(sqrt(((sqrt(2)! + 0! + 0!)! – 0!)!))

100 = flooring(sqrt((2 + 0! + 0!)!)!) – 0!

It ought to be famous that copying one of many above formulation into WolframAlpha may not give the suitable reply. This is as a result of it interprets ‘!!’ because the “double factorial operate”: n!! = n(n-2)(n-4)…, the place I take advantage of n!! to imply (n!)!. Putting areas between the exclamation factors ought to repair this.