If we take F=ma then we get Kg*m/s^2. If we take (for whatever reason) 1m+1s:
1--what is the result?
2--what are the units of measurement?
3--how can we interpret this units of measurement for the sum of 1m+1s in English with just words? For the derivative we say: "the derivative is the rate of change". What is the addition of units of measurement? The problem is that mathematics in general has no units of measurement and in order for me to gain deeper understanding of it I need units. You know?

Thank you

  • $\begingroup$ 1. DNE. 2. DNE. 3. DNE. $\endgroup$ – Did Jul 28 '17 at 11:39
  • $\begingroup$ why would one consider such a thing? $\endgroup$ – Lord Shark the Unknown Jul 28 '17 at 11:39
  • $\begingroup$ the real problem here is 1 could be units over units let s say we have x=1m+1s divide both sides by s and we get: $${x\over s}=1{m\over s}+1\\{xy-y\over sy}=1{m\over s}$$ if we let sy=s we get y=1 again and get x-1 on the top. if y has units per second then seconds gets cancelled out of the denominator potentially ( unless y has units per second squared) etc. $\endgroup$ – user451844 Jul 28 '17 at 12:06
  • $\begingroup$ I see, but what I am trying to understand is how to interpret 1m+1s in English. You know. Every formula and expression can be told to someone in words. For the derivative you will say to someone: "the derivative is the rate of change". How can we explain 1m+1s? 1ms shows that our quantity is proportional to length and time. It is a multiplication. What is the addition of units of measurement? $\endgroup$ – Dimitrios Efthymiou Jul 28 '17 at 12:20
  • $\begingroup$ "Every formula and expression can be told to someone in words". Yes, but of course not everything that can be told by words makes sense. For instance, I do not feel compelled to make sense of "every booklet terminates Jenny's bell tomorrow", or of "horse battery staple correct". $\endgroup$ – user228113 Jul 28 '17 at 13:15

Think of units like variables: the expression $2x+3y$ can't be simplified further, and in exactly the same way, if you write $1$m $+ 1$s, you can't write it as a single term.

It's adding 1 potato + 1 pillow: they're not the same kind of thing.

  • $\begingroup$ Hmm. OK. I guess we can go one level up in abstraction. For example 1apple+2oranges=3fruits. So for multiplication we say 1ms (1 metersecond or whatever), but for addition we just leave it as it is $\endgroup$ – Dimitrios Efthymiou Jul 28 '17 at 11:59
  • $\begingroup$ If we calculate the vector magnitude for a vector u={1m, 1s} then we can see that the length is 1.414 but what if we have units of measurement like meters and seconds? What will the vector magnitude be, with what unit of measurement and how can we interpret that? $\endgroup$ – Dimitrios Efthymiou Jul 28 '17 at 12:07

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