reader to try to provide either a proof or a strategy for developing natural numbers beyond 10. To assist in this endeavor I have listed constructions from 11 to 30. List of constructions for 11 through 30 4/,4 + 4/4
= 11
4! – (4 – 4/4)
= 21
(44 + 4)/4
= 12
44/(4/√4)
= 22
44/4 + √4
= 13
4! – 4(4 – 4)
= 23
4/.4 +√4 + √4
= 14
44 – 4! + 4
= 24
44/4 + 4
= 15
4! +4(4 – 4)
= 25
4+4+4+4
= 16
4! + (4 + 4)/4
= 26
4 x 4 + 4/4
= 17
4! + 4 – 4/4
= 27
4 x 4 + 4√4
= 18
4! + 4 – (4 – 4)
= 28
4! – ( 4 + 4/4)
= 19
4! + (4 + 4/4)
= 29
4/.4 + 4/.4
= 20
4! + (4 + 4/√4)
= 30
Many of the constructions from 31 to 41 require the use of the Greatest Integer Function (INT). For example, one construction for 31 is: INT(4!/√√.4 + 4/4) and a construction for 41 is: INT(4!/√.4 + √4 + √4). Constructions for 42 through 50 are relatively easy. For example, a construction for 42 is: 44 – 4/√4 and a construction for 50 is: 44 + 4 +√4. Constructions for 51 through 100 are both hard and easy. For example, a construction for 53 is: INT(4!/√.4 + 4 x 4), while 100 can easily be expressed as: (4/.4) x (4/.4). Again, my challenge to the reader is two fold. Can you develop a construction for all natural numbers from 1 to100 and can you come up with a proof that any natural number can be constructed as Dr Wilkins suggested. I have already given you a good head start. Dr. Wilkins gave an elegant construction for 1000. i.e. 4 x 44 - 4!
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