Spaces:
Sleeping
Sleeping
Add sets notebook to probability series
Browse files
data_science/00.01-set-theory-fundamentals.py
ADDED
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1 |
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# /// script
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# requires-python = ">=3.10"
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# dependencies = [
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# "marimo",
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# ]
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# ///
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import marimo
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__generated_with = "0.10.17"
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app = marimo.App()
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+
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+
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@app.cell(hide_code=True)
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def _(mo):
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mo.md(
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"""
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+
# 🎯 Set Theory: The Building Blocks of Probability
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+
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Welcome to the magical world of sets! Think of sets as the LEGO® blocks of probability -
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they're the fundamental pieces we use to build more complex concepts.
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+
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## What is a Set?
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A set is a collection of distinct objects, called elements or members.
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For example:
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+
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- 🎨 Colors = {red, blue, green}
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+
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- 🔢 Even numbers under 10 = {2, 4, 6, 8}
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- 🐾 Pets = {dog, cat, hamster, fish}
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"""
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)
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return
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@app.cell
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def _(elements):
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elements
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return
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@app.cell(hide_code=True)
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def _(mo):
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# interactive set creator
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elements = mo.ui.text(
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value="🐶,🐱,🐹",
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label="Create your own set (use commas to separate elements)"
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)
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return (elements,)
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@app.cell(hide_code=True)
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def _(elements, mo):
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user_set = set(elements.value.split(','))
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mo.md(f"""
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### Your Custom Set:
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${{{', '.join(user_set)}}}$
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Number of elements: {len(user_set)}
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""")
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return (user_set,)
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@app.cell(hide_code=True)
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def _(mo):
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mo.md(
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"""
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## 🎮 Set Operations Playground
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Let's explore the three fundamental set operations:
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+
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- Union (∪): Combining sets
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- Intersection (∩): Finding common elements
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- Difference (-): What's unique to one set
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Try creating two sets below!
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"""
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)
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return
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@app.cell
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def _(operation):
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operation
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return
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@app.cell(hide_code=True)
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def _(mo):
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set_a = mo.ui.text(value="🍕,🍔,🌭,🍟", label="Set A (Fast Food)")
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set_b = mo.ui.text(value="🍕,🥗,🥙,🍟", label="Set B (Healthy-ish Food)")
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operation = mo.ui.dropdown(
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options=["Union", "Intersection", "Difference"],
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value="Union",
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label="Choose Operation"
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)
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return operation, set_a, set_b
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@app.cell
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def _(mo, operation, set_a, set_b):
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A = set(set_a.value.split(','))
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B = set(set_b.value.split(','))
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results = {
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"Union": (A | B, "∪", "Everything from both sets"),
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"Intersection": (A & B, "∩", "Common elements"),
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"Difference": (A - B, "-", "In A but not in B")
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}
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_result, symbol, description = results[operation.value]
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+
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mo.md(f"""
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### Set Operation Result
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+
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$A {symbol} B = {{{', '.join(_result)}}}$
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+
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**What this means**: {description}
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+
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**Set A**: {', '.join(A)}
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**Set B**: {', '.join(B)}
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""")
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return A, B, description, results, symbol
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+
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+
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@app.cell(hide_code=True)
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135 |
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def _(mo):
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mo.md(
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+
"""
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138 |
+
## 🎬 Netflix Shows Example
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139 |
+
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140 |
+
Let's use set theory to understand content recommendations!
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141 |
+
"""
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142 |
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)
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143 |
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return
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144 |
+
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+
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146 |
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@app.cell
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147 |
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def _(viewer_type):
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148 |
+
viewer_type
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149 |
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return
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+
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151 |
+
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152 |
+
@app.cell
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153 |
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def _(mo):
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154 |
+
# Netflix genres example
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155 |
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action_fans = {"Stranger Things", "The Witcher", "Money Heist"}
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156 |
+
drama_fans = {"The Crown", "Money Heist", "Bridgerton"}
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157 |
+
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158 |
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viewer_type = mo.ui.radio(
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159 |
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options=["New Viewer", "Action Fan", "Drama Fan"],
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160 |
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value="New Viewer",
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161 |
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label="Select Viewer Type"
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162 |
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)
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163 |
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return action_fans, drama_fans, viewer_type
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164 |
+
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165 |
+
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166 |
+
@app.cell
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167 |
+
def _(action_fans, drama_fans, mo, viewer_type):
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168 |
+
recommendations = {
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169 |
+
"New Viewer": action_fans | drama_fans, # Union for new viewers
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170 |
+
"Action Fan": action_fans - drama_fans, # Unique action shows
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171 |
+
"Drama Fan": drama_fans - action_fans # Unique drama shows
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172 |
+
}
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173 |
+
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174 |
+
result = recommendations[viewer_type.value]
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175 |
+
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176 |
+
explanation = {
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177 |
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"New Viewer": "You get everything to explore!",
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178 |
+
"Action Fan": "Pure action, no drama!",
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179 |
+
"Drama Fan": "Drama-focused selections!"
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180 |
+
}
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181 |
+
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182 |
+
mo.md(f"""
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183 |
+
### 🎬 Recommended Shows
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184 |
+
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185 |
+
Based on your preference for **{viewer_type.value}**, we recommend:
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186 |
+
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187 |
+
{', '.join(result)}
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188 |
+
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189 |
+
**Why these shows?**
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190 |
+
{explanation[viewer_type.value]}
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191 |
+
""")
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192 |
+
return explanation, recommendations, result
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193 |
+
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194 |
+
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195 |
+
@app.cell(hide_code=True)
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196 |
+
def _(mo):
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197 |
+
mo.md(
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198 |
+
"""
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199 |
+
## 🧮 Set Properties
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200 |
+
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201 |
+
Important properties of sets:
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202 |
+
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203 |
+
1. **Commutative**: A ∪ B = B ∪ A
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204 |
+
2. **Associative**: (A ∪ B) ∪ C = A ∪ (B ∪ C)
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205 |
+
3. **Distributive**: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
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206 |
+
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207 |
+
Let's verify these with a fun exercise!
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208 |
+
"""
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209 |
+
)
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210 |
+
return
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211 |
+
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212 |
+
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213 |
+
@app.cell
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214 |
+
def _(mo, property_check, set_size):
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215 |
+
mo.hstack([property_check, set_size])
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216 |
+
return
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217 |
+
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218 |
+
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219 |
+
@app.cell
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220 |
+
def _(mo):
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221 |
+
# Interactive property verifier
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222 |
+
property_check = mo.ui.dropdown(
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223 |
+
options=[
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224 |
+
"Commutative (Union)",
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225 |
+
"Commutative (Intersection)",
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226 |
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"Associative (Union)"
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227 |
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],
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228 |
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value="Commutative (Union)",
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229 |
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label="Select Property to Verify"
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230 |
+
)
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231 |
+
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232 |
+
set_size = mo.ui.slider(
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233 |
+
value=3,
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234 |
+
start=2,
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235 |
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stop=5,
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236 |
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label="Set Size for Testing"
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237 |
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)
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238 |
+
return property_check, set_size
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239 |
+
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240 |
+
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241 |
+
@app.cell
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242 |
+
def _(mo, property_check, set_size):
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243 |
+
import random
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244 |
+
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245 |
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# Create random emoji sets for verification
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246 |
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emojis = ["😀", "😎", "🤓", "🤠", "😴", "🤯", "🤪", "😇"]
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247 |
+
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248 |
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set1 = set(random.sample(emojis, set_size.value))
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249 |
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set2 = set(random.sample(emojis, set_size.value))
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250 |
+
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operations = {
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252 |
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"Commutative (Union)": (
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253 |
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set1 | set2,
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254 |
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set2 | set1,
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"A ∪ B = B ∪ A"
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),
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257 |
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"Commutative (Intersection)": (
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set1 & set2,
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set2 & set1,
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260 |
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"A ∩ B = B ∩ A"
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),
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262 |
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"Associative (Union)": (
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263 |
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(set1 | set2) | set(random.sample(emojis, set_size.value)),
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264 |
+
set1 | (set2 | set(random.sample(emojis, set_size.value))),
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265 |
+
"(A ∪ B) ∪ C = A ∪ (B ∪ C)"
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266 |
+
)
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267 |
+
}
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268 |
+
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269 |
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result1, result2, formula = operations[property_check.value]
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270 |
+
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271 |
+
mo.md(f"""
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272 |
+
### Property Verification
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273 |
+
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274 |
+
**Testing**: {formula}
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275 |
+
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276 |
+
Set A: {', '.join(set1)}
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277 |
+
Set B: {', '.join(set2)}
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278 |
+
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279 |
+
**Left Side**: {', '.join(result1)}
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280 |
+
**Right Side**: {', '.join(result2)}
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281 |
+
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282 |
+
**Property holds**: {'✅' if result1 == result2 else '❌'}
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283 |
+
""")
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284 |
+
return emojis, formula, operations, random, result1, result2, set1, set2
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285 |
+
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286 |
+
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287 |
+
@app.cell(hide_code=True)
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288 |
+
def _(mo):
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289 |
+
quiz = mo.md("""
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290 |
+
## 🎯 Quick Challenge
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291 |
+
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292 |
+
Given these sets:
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293 |
+
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294 |
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- A = {🎮, 📱, 💻}
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295 |
+
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296 |
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- B = {📱, 💻, 🖨️}
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297 |
+
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298 |
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- C = {💻, 🖨️, ⌨️}
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299 |
+
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300 |
+
Can you:
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301 |
+
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302 |
+
1. Find all elements that are in either A or B
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303 |
+
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304 |
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2. Find elements common to all three sets
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305 |
+
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306 |
+
3. Find elements in A that aren't in C
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307 |
+
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308 |
+
<details>
|
309 |
+
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310 |
+
<summary>Check your answers!</summary>
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311 |
+
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312 |
+
1. A ∪ B = {🎮, 📱, 💻, 🖨️}<br>
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313 |
+
2. A ∩ B ∩ C = {💻}<br>
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314 |
+
3. A - C = {🎮, 📱}
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315 |
+
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316 |
+
</details>
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317 |
+
""")
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318 |
+
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+
mo.callout(quiz, kind="info")
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320 |
+
return (quiz,)
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321 |
+
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322 |
+
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323 |
+
@app.cell(hide_code=True)
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324 |
+
def _(mo):
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325 |
+
callout_text = mo.md("""
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326 |
+
## 🎯 Set Theory Master in Training!
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327 |
+
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328 |
+
You've learned:
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329 |
+
|
330 |
+
- Basic set operations
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331 |
+
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332 |
+
- Set properties
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333 |
+
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334 |
+
- Real-world applications
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335 |
+
|
336 |
+
Coming up next: Axiomatic Probability! 🎲✨
|
337 |
+
|
338 |
+
Remember: In probability, every event is a set, and every set can be an event!
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339 |
+
""")
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340 |
+
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341 |
+
mo.callout(callout_text, kind="success")
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342 |
+
return (callout_text,)
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343 |
+
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344 |
+
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345 |
+
@app.cell
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346 |
+
def _():
|
347 |
+
import marimo as mo
|
348 |
+
return (mo,)
|
349 |
+
|
350 |
+
|
351 |
+
if __name__ == "__main__":
|
352 |
+
app.run()
|