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Why can't we list every single number (including decimals) the orange line covers?

a) There are too many numbers to list.
b) The orange line represents negative numbers only.
c) It is not possible to graph all numbers.
d) The orange line covers specific fractions.

1 Answer

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Final answer:

The orange line with a positive slope represents an infinite series of numbers, which cannot be listed completely due to their infinite nature and impracticality. Estimation is often used as a practical alternative.

Step-by-step explanation:

We cannot list every single number (including decimals) the orange line covers due to the nature of continuous number lines in mathematics. If given that the line has a positive slope and moves downwards as the x-value increases, it suggests that we are referring to an infinite set of numbers. This is because between any two points on a line, there are infinitely many decimal numbers. Additionally, certain numbers may have an infinite number of decimal places, making it impossible to list them all.



Considering a horizontal line at a positive or negative value, this line would still represent an infinite number of points along that specific value, and it is simply not practical or possible to write out every decimal that exists on this continuous line.



In practice, we often round or estimate numbers to a manageable number of decimal places because listing out an infinite series of decimals would take an infinite amount of time and resources. Not only is it impractical, but it's rarely beneficial for finding better solutions, as most real-world applications are tolerant of some level of estimation.

User Jim Geurts
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