In binary the one on the left is meaningless, and therefore the two cannot be compared. In any base in which they can be compared, the one on the left is smaller.
Fractional bases are weird, and I think there's even competing standards. What I was thinking is that you can write any number in base n like this:
\sum_{k= -∞}^{∞} a_k * n^k
where a_k are what we would call the digits of a number. To make this work (exists and is unique) for a given positive integer base, you need exactly n different symbols.
For a base 1/n, turns out you also need n different symbols, using this definition. It's fairly easy to show that using 1/n just mirrors the number around the decimal point (e.g. 13.7 becomes 7.31)
I am not very well versed in bases tho (unbased, even), so all of this could be wrong.
Obviously he is correct because the smallest base that can represent 10 is base 2 and 10 in base 2 is equal to 2 in base 10. And the smallest base in which you can represent the number 3 is base 4 and 3 in base 10 in equal to 3 so 2 is the smaller number hence "10" is the smaller number. And from the drawing of the rainbow you can infer that he wants to use a diverse range of bases and not just the common base 10. Btw I am only talking about the natural bases (whole number positive).
By some definitions, maybe. However, definitions that exclude it probably do so for a specific reason. It's more a fluke of categorization than a real world distinction. Those distinctions might be critical to certain logic systems, but even most people who use that definition recognize reality.
Zero is a number in more cases than it isn't. It is a symbol that represents a value. Just like infinity, it doesn't matter if 0 doesn't exist in physical reality. It's still a useful value in most cases.
they never specified the order relation, so we can’t really know what they meant by smallest. for all we know, 10 could be the right answer
What are you supposed to write there? I guess 3 < 10 is not the answer. It also requires text, so drawing 3 vs 10 of something isn't suitable, too. "You taught us" or what do they want to hear??
i think when it says ‘or show’ it allows a drawing
id probably put dots … ………. then circle the bigger one
I imagine you might say that 10 has two digits, so it has to be bigger. Or maybe you can list out the first 10 numbers in order.
