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You could also add this non-mathematical example: when I say “We have the same toy”, I mean both our toys are the same; but when I say “We have the same mother”, I mean that both are mothers point to the same exact object. Important distinction, I think; and one I first realized via programming (when 2 objects have equal values, but are not the same thing is one case; and when 2 names, as in Python where we don’t really have any variables per se, point to the same object in memory, akin to ByRef in more primitive languages, is the second).
Thanks Yatharth, great point. And a funny thought – in the math world, are we all using the same number 17, or different copies of it?
I feel uneasy about an area being equal to a different type quantity, e.g., a volume etc., even if numerically equal Are there times in maths where different quantities can be equal?
Hi Fiona, great question. In algebra, technically we don’t have any units, so 3, x, x^2, 15x^3 are all of the same.
For example, if x = 3, then x^2 = 9, and they can be compared directly. We might have an equation like x^2 - x = 6 and solve it to see that x=3 (or -2). The various powers can interact.
However, in certain applications, like physics, we might keep track of units (length, area, volume, etc.) and then realize we can’t mix the results.
I do not have much knowledge of programming. Can you explain me the differences between =; ==; and ===? Thanks for your answer.
Thanks for comment, I thought it should be mentioned in here .
@Ondřej: Sure thing. In programming, = is assignement, so x = 3 assigns the number 3 to the variable x.
== is a check for equality, so x == 3 is checking whether x already equals 3 (and results in true or false).
=== is a strict check for equality ,where x must be the number 3 and not the character “3”. In some programming scenarios, characters are automatically converted to their numeric equivalent where possible, and === is making sure that isn’t happening.