For (c), let’s parse that sentence. Mathematicians have a way of making simple things complex. “f(S) is the smallest integer i such that the ith bit of S is 1 and f(S)=0 when S is the empty string, the string with no bits.” This is saying something like… suppose you have a bit string. And suppose the first position in it is “bit 1,” and second position contains “bit 2,” the third “bit 3” and so on. Each of those bits is a 0 or a 1. For each bit string, find the 1 in the lowest position. The number value of the position is the element of the codomain to which that bit string maps. So, for example, for a given bit string, if the first 1 you encounter is in position 3, that bit string maps to 3 in the codomain.
For (c), let’s parse that sentence. Mathematicians have a way of making simple things complex. “f(S) is the smallest integer i such that the ith bit of S is 1 and f(S)=0 when S is the empty string, the string with no bits.” This is saying something like… suppose you have a bit string. And suppose the first position in it is “bit 1,” and second position contains “bit 2,” the third “bit 3” and so on. Each of those bits is a 0 or a 1. For each bit string, find the 1 in the lowest position. The number value of the position is the element of the codomain to which that bit string maps. So, for example, for a given bit string, if the first 1 you encounter is in position 3, that bit string maps to 3 in the codomain.
For (c), let’s parse that sentence. Mathematicians have a way of making simple things complex. “f(S) is the smallest integer i such that the ith bit of S is 1 and f(S)=0 when S is the empty string, the string with no bits.” This is saying something like… suppose you have a bit string. And suppose the first position in it is “bit 1,” and second position contains “bit 2,” the third “bit 3” and so on. Each of those bits is a 0 or a 1. For each bit string, find the 1 in the lowest position. The number value of the position is the element of the codomain to which that bit string maps. So, for example, for a given bit string, if the first 1 you encounter is in position 3, that bit string maps to 3 in the codomain.For (c), let’s parse that sentence. Mathematicians have a way of making simple things complex. “f(S) is the smallest integer i such that the ith bit of S is 1 and f(S)=0 when S is the empty string, the string with no bits.” This is saying something like… suppose you have a bit string. And suppose the first position in it is “bit 1,” and second position contains “bit 2,” the third “bit 3” and so on. Each of those bits is a 0 or a 1. For each bit string, find the 1 in the lowest position. The number value of the position is the element of the codomain to which that bit string maps. So, for example, for a given bit string, if the first 1 you encounter is in position 3, that bit string maps to 3 in the codomain.
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