Tag Archives: equivalence classes

[G]eometry and number[s]…are unified by the concept of a coordinate system, which allows one to convert geometric objects to numeric ones or vice versa. … [O]ne can view the length ❘AB❘ of a line segment AB not as a number … Continue reading

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[T]he point of introducing L^p spaces in the first place is … to exploit … Banach space. For instance, if one has |ƒ − g| = 0, one would like to conclude that ƒ = g. But because of the … Continue reading

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Leonardo da Vinci’s ability to embrace uncertainty, ambiguity, and paradox was a critical characteristic of his genius. —J Michael Gelb Say you want to use a mathematical metaphor, but you don’t want to be really precise. Here are some ways … Continue reading

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Do numbers exist?

When I was a math teacher some curious students (Fez and Andrew) asked, “Does i, √−1, exist? Does infinity ∞ exist?” I told this story. You explain to me what 4 is by pointing to four rocks on the ground, … Continue reading

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