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1 Logic

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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

Wormate.io 3.3.3 May 2026

Wormate.io version 3.3.3 is a legacy version of the popular multiplayer snake-style action game developed by Oleksandr Godoba. As of 2026, the game has evolved significantly, with modern versions reaching version 4.0.23. Technical Specifications (v3.3.3 context)

For the first time, he wasn’t prey. He weaved through the giants, watching them eat each other’s tails. QueenCrumb lunged at VortexKing. VortexKing dodged—right into Glitch’s suddenly expanded hitbox. BOOM. 10,000 points dissolved into rainbow sprinkles.

The Gourmet Diet: Prioritize cakes, donuts, and chocolate biscuits over basic sweets to grow significantly faster. wormate.io 3.3.3

• Improved Graphics: The game's graphics have been enhanced, providing a more immersive and visually appealing experience.
• New Power-Ups: Players can now collect power-ups, such as speed boosts and shields, to gain an advantage over their opponents.
• Enhanced Gameplay: The game's mechanics have been fine-tuned, providing a more responsive and engaging gameplay experience.

Conclusion

Rating: 4.6/5
Best for: Mobile gamers with average internet speeds.
Avoid if: You hate visual clutter (the neon pets are bright). Wormate

What's new in 3.3.3?

Grow by Eating: Consume sweets like cakes, chocolate biscuits, and candies to increase your size. Improved Graphics : The game's graphics have been

Black Screen on Launch

This occurs if you are running Android 14 or iOS 17 with an older cache. Force stop the app, clear cache (not data), and restart. For version 3.3.3 specifically, ensure your OS is up to date.