Why Do We Add 1 When Counting Numbers Between Two Integers?

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AI Thread Summary
When counting the numbers between two integers, such as from 27 to 63, the formula used is 63 - 27 + 1. The addition of 1 accounts for including both the starting number (27) and the ending number (63) in the total count. Without adding 1, the count would only reflect the numbers between the two integers, excluding one of the endpoints. This principle applies universally in counting ranges, ensuring both endpoints are considered. Understanding this concept clarifies why the "+1" is necessary in the calculation.
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Homework Statement


so we have from 27... 63 we want ot calcul how much numbers in there
i was looking in the book and saw 63 -27 + 1 , now this might sound very simple but i got confused why do we add the"1" please explain..
PS:this is astupid uestion i know but it's weird it confused me ..


Homework Equations





The Attempt at a Solution


63-27
 
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Andrax said:

Homework Statement


so we have from 27... 63 we want ot calcul how much numbers in there
i was looking in the book and saw 63 -27 + 1 , now this might sound very simple but i got confused why do we add the"1" please explain..
PS:this is astupid uestion i know but it's weird it confused me ..


Homework Equations





The Attempt at a Solution


63-27

Not a calculus question, should be in Precalc.

OK, how many numbers from 1 to 5 (including both the starting and ending numbers)?

Is it just 5 - 1? Or is it 5 - 1 PLUS 1?

Same principle when you count from 27 to 63. If you don't add the 1, you're neglecting the starting number.
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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