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Reading set notation

by James Martini

Categories: Journal

Tags: math, mathml, notation

Comments: Comments Off

Published on: June 25, 2009

So I’ve been skipping my World of Warcraft time and reviewing calculus and differential equations so I don’t get too rusty. I almost immediately ran into an issue “reading” some of the set notation. It’s great because it’s compact and can communicate a lot of information but that doesn’t help if you can’t read it.

Take for example

{(x,f(x))|x∈A}

Doesn’t say much unless you can read it as “the set of all ordered pair x, f of x such that x is a member of set A”. Here are a few quick rules:

{ } denotes the set
( ) denotes and ordered pair
| “such that”
: also “such that” just in case things were too clear
∈ “is a member of”
∉ “is not a member of”
∪ union of two sets
∩ intersection of sets

So ℕ = {|a| : a ∈ ℤ} reads as “The set of natural numbers is equal to the absolute value of a such that a is a member of set ℤ”. Since ℤ is generally the set of ingeters { … ,-2, -1, 0, 1, 2, … } this means that ℕ = {0, 1, 2, … }

So now I can mostly read set notation again. Now I just need to learn MathML.

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from sklearn import neighbors, datasets, preprocessing
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from sklearn.metrics import accuracy_score

# load the data into training and test sets
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from sklearn import neighbors, datasets, preprocessing

from sklearn.model_selection import train_test_split

from sklearn.metrics import accuracy_score

# load the data into training and test sets

iris = datasets.load_iris()

X, y = iris.data[:, :2], iris.target

X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=13)

# scale the data

scaler = preprocessing.StandardScaler()

scaler.fit(X_train)

X_train = scaler.transform(X_train)

X_test = scaler.transform(X_test)

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knn = neighbors.KNeighborsClassifier(n_neighbors = 5)

knn.fit(X_train, y_train)

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