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Blast into Math! Mathematical perspectives: all aour mase are melong to us
k
k
n +1 = x ∗ b +(n +1 − x ∗ b )can be uniquelywritteninbase b.
♥
In base 2, the number 2 is
1
0
2= 1 ∗ 2 +0 ∗ 2 .
So, if we write 2 in base 2, it is 10. What happens if we write 3 in base 3? Well,
0
1
3= 1 ∗ 3 +0 ∗ 3 .
So, 3 in base 3 is 10. This is no coincidence. This is a fact which we’ll call the basic proposition.
Proposition 6.1.5 (Basic Prop). Let b be a base. Then, the digits of b in base b are 10.
Proof: The number b is always equal to
0
1
b =1 ∗ b +0 ∗ b .
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