Determining Particular Values of a Variable

Recall our candy example from section 3.2. In this example, we talked about picking a candy out of a bag. Without looking at the candy, we could give it a variable name "The Candy in My Hand", and make some statements about it.

But what happens when we open our hand? Now we find out which object is actually associated with the variable "The Candy in my Hand" on this particular occasion. Now we know that, in this particular case, "The Candy in my Hand" is a green jelly bean. We can then pick another candy from the bag, which becomes the next "The Candy in my Hand". This time it turns out that "The Candy in my Hand" is a red gummy bear.

Similarly, the same mathematical variable name can label one mathematical object at one time, and another mathematical object at another. This is where the idea of equality comes in to play once again. When we want to indicate that a variable at this moment in time has a certain mathematical object- for instance, a certain number- associated with it, we say that the variable equals that number. For example, at a certain point in time we might say "the variable x equals five". This is written symbolically as "x = 5".

This lets us describe the connection between a general mathematical equation and a particular situation that is an example of that equation.

We can take the general equation:

day1 + day2 + day3 + day4 + day5 + day6 + day7 = total_precipitation

and say, when talking about the first week of April

day1 = 0.2
day2 = 1.0
day3= 0
day4= 0
day5= 0.4
day6= 0
day7= 0.3
total_precipitation= 1.9 ml

However, when we are talking about the first week of November we can say

day1 = 0.5
day2 = 0.1
day3= 0.1
day4= 0.2
day5= 0
day6= 0
day7= 0.3
total_precipitation= 1.1 ml

In this case, the variable names stay the same, but at different times they label different numbers. When dealing with variables it's important to know that the same variable name can be equal to different numbers at different times, and keep track of what the variable equals at the particular time you are using it.

It can also be useful to ask yourself what sorts of mathematical objects the variable could never equal. In this case the total_precipitation variable for the first week of November would probably never equal 120, because there have never been 120 ml of precipitation in Eureka in the first week of November.

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