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Essence of Math

Toolness Of Math

The Number Line

Fractions

Negative Numbers

Irrational Numbers

Variables

Equations

Functions

Modulus

Binary Numbers

Complex Plane

PDE

Essence of Math

Toolness Of Math

The Number Line

Fractions

Negative Numbers

Irrational Numbers

Variables

Equations

Functions

Modulus

Binary Numbers

Complex Plane

PDE

Ultimate Space = S

s_{i} = arbitrary partition of S

Δs_{i} = infinitesimal s_{i}, that is limit of s_{i} as it tends to zero.

p_{i} = arbitrary point in S = Δs_{i}

**Problem 41**: what is a normed linear space?
**Ans: let X be a linear space over the field F where F is either the real field R or the complex field C.
A norm on X is a real-valued function whose value at x is denoted by ||x||, satisfying the following conditions for all x, y, in X and &lpha; in F:
(i)||x|| > 0 if x ≠ 0
(ii)||αx|| = |α|||x||
(iii)||x + y|| ≤ ||x|| + ||y||
A linear space X with a norm defined on it is called a normed linear space. **

**Problem 42**: Consider a vector space with origin at O in which the vector **u** is represented by the arrow from O to P and the vector **v** is represented by the arrow from O to Q. The projection of
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**Problem 43**:
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**Problem 44 **:
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**Problem 45 **:
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**Problem 46**:

**Problem 47**:
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**Problem 48**:
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**Problem 49**:
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**Problem 50**:
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Peter Oye Sagay