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etotheipi

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## Main Question or Discussion Point

This topic is quite confusing. For instance, if I write ##14_6##, do I pronounce this as "ten", even though we'd probably just say "one-four, base six"? That is to say that we'd treat "ten" as a number of things that we could count out (i.e. corresponding to a certain number of sticks).

Another point, if we again consider the number ##14_6##, then this would correspond to one lot of six sticks and 4 lots of single sticks, where we've defined one, two, three, ..., nine to be known numbers of things. This is often written as

##14_6 = 1 \times 6 + 4 \times 1##

but isn't this construction preemptively implying that we are using base ten? Another example might be

##B3_{16} = 11 \times 16 + 3 \times 1##

Do we only write it like this since we've memorised a certain amount of computations in base ten (e.g. times tables) so it is convenient to use base ten as a middle-man for all calculations?

Is it perhaps because our language system is built around base ten, i.e. twenty two ##\equiv## 22, thirty six ##\equiv## 36, etc.?

Another point, if we again consider the number ##14_6##, then this would correspond to one lot of six sticks and 4 lots of single sticks, where we've defined one, two, three, ..., nine to be known numbers of things. This is often written as

##14_6 = 1 \times 6 + 4 \times 1##

but isn't this construction preemptively implying that we are using base ten? Another example might be

##B3_{16} = 11 \times 16 + 3 \times 1##

Do we only write it like this since we've memorised a certain amount of computations in base ten (e.g. times tables) so it is convenient to use base ten as a middle-man for all calculations?

Is it perhaps because our language system is built around base ten, i.e. twenty two ##\equiv## 22, thirty six ##\equiv## 36, etc.?