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Start with, tan(x) = cot(90-x).
Sorry for asking too many questions.
Say x=2.0, then (1.95 ≤ x ≤ 2.05). If the two bounds are not exact, then they can be expressed further as (1.945 ≤ 1.95 ≤ 1.955) and (2.045 ≤ 2.05 ≤ 2.055), and continuing indefinitely results, 1.944444444... ≤ 1.95 ≤ x ≤ 2.05 ≤ 2.055555555... => 1.944444444... ≤ x ≤ 2.055555555...
And I find no reason why the bounds should be inexact, i.e. consisting of three significant digits.
x and y have different errors. You are going way past what is required. You only need to apply the definition in post #4 to understand this.
What about x=2.0≤2.05, y=2.05≤2.055, and x≤2.055?
If x ≤ 2.05 then of course x ≤ 2.055. What does that have to do with what we are doing?
If so, then x ≤ 2.055555555... That's why I asked whether 2.05 was an ordinary number or a number with three significant figures.
What about x=2.0≤2.05, y=2.05≤2.055, and x≤2.055?
I still don't get it. If 1.95≤x=2.0, and if 1.945≤y=1.95, I know that y≤x, but why not 1.945≤x?
Is it because if 1.945 is rounded to two significant figures, it's 1.9 instead of (2.0)?
I mean if x=2.0, then (1.95 ≤ x ≤ 2.05). But is it the case (a) or (b)?
a) 1.950000000000 ≤ x ≤ 2.050000000000 (with infinite number of significant digits)
or b) 1.945 ≤ x ≤ 2.055
Sorry, I meant x=2.0
So even though 1.95 is any value between 1.945 and 1.955, x remains (1.950 ≤ x).
Or is this (1.945 ≤ x) correct?
I'm a bit confused...
2.05 is no more exact then 1.95. They both have 3 significant digits.
4 is an example of an exact number.
If each of 1.95 and 2.05 has three significant figures, then 1.95 is any value between 1.945 and 1.955, and for x: 1.945 ≤ x, which is wrong since 1.95 ≤ x.
No I haven't, but the table of contents is:
0 Precalculus Review
1 Functions and Applications
2 The Mathematics of Finance
3 System of Linear Equations and Matrices
4 Matrix Algebra and Applications
5 Linear Programming
6 Sets and Counting
7 Probability
8 Random Variables and Statistics
9 Nonlinear Functions and Models
10 Introduction to the Derivative
11 Techniques of Differentiation with Applications
12 Further Applications of the Derivative
13 The Integral
14 Further Integration Techniques and Applications of the Integral
15 Functions of Several Variables
16 Trigonometric Models
I want to self-study a range of topics, from pre-algebra to calculus.
I've many gaps in mathematics, therefore I want, starting from the bottom, to re-learn some topics. Can you recommend me a book which covers many different topics and gives proofs for some rules? I have thought of buying "Finite Math and Applied Calculus" by Stefan Waner and Steven Costenoble.
What does being exact mean then? The more significant digits, the more exact a number is? In this context, is exact a synonym to accurate?
In pure mathematics, say x=2.01, isn't x an exact number?
Thank you. So x=2.0 means that 1.95 ≤ x ≤ 2.05, while 1.95 and 2.05 being exact numbers.
An exact number is a number with an infinite number of significant digits. Am I thinking right?