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1 Logic

• Reveries
• 8liam.7z
• 78875x
• Ma.7z
• Breast

2 Proofs

• 1. Direct Proofs
• 2. Divisibility
• 3. Existence proofs
• 4. Induction
• 5. Uniqueness Arguments
• 6. Indirect Proof

3 Number Theory

• 1. Congruence
• 2. $\Z_n$
• 3. The Euclidean Algorithm
• 4. $\U_n$
• 5. The Fundamental Theorem of Arithmetic
• 6. The GCD and the LCM
• 7. The Chinese Remainder Theorem
• 8. The Euler Phi Function
• 9. The Phi Function—Continued
• 10. Wilson's Theorem and Euler's Theorem
• 11. Public Key Cryptography
• 12. Quadratic Reciprocity

4 Functions

• 1. Definition and Examples
• 2. Induced Set Functions
• 3. Injections and Surjections
• 4. More Properties of Injections and Surjections
• 5. Pseudo-Inverses
• 6. Bijections and Inverse Functions
• 7. Cardinality and Countability
• 8. Uncountability of the Reals
• 9. The Schröder-Bernstein Theorem
• 10. Cantor's Theorem

5 Relations

• 1. Equivalence Relations
• 2. Factoring Functions
• 3. Ordered Sets
• 4. New Orders from Old
• 5. Partial Orders and Power Sets
• 6. Countable total orders

6 Bibliography

Sugar Paradise - Teen

"The clock strikes midnight in Sugar Paradise, and the neon licorice signs begin to flicker. You stand at the edge of the Taffy Docks, the scent of blue raspberry heavy in the humid air. Your phone buzzes—a message from an unknown sender. 'Meet me at the Lemon Drop Lounge. It's time to show them that paradise has a bitter end.' You adjust your goggles, kick your board into gear, and head toward the glow. In this world, you either blend in or you melt away."

: The skyline is dominated by the Marzipan Towers , glowing with soft pastel lights. To the north lies the Soda Pop Sea , where the tides hum with carbonation, and to the south, the Gummy Forests offer a shifting, translucent maze for those looking to disappear. sugar paradise teen

Welcome to , a neon-soaked, crystalline world where the air smells like spun sugar and the streets are paved with iridescent rock candy. For the teenagers who live here, it's not just a sweet escape—it's a high-stakes social playground where your flavor profile determines your status. "The clock strikes midnight in Sugar Paradise, and

: Behind the sweetness lies the Sour Rebellion . Not everyone wants to live in a world of artificial perfection. A group of "Sour" teens has started tagging the pristine candy walls with neon citrus graffiti, fighting for a world that has a little more "bite" and a lot less syrup. Sample Hook for a Story or Roleplay 'Meet me at the Lemon Drop Lounge

: It’s "candypunk"—a mix of sugary aesthetics and rebellious teen energy. Think oversized hoodies in sherbet colors, holographic accessories, and hoverboards that leave trails of glitter-dust.