SINIMULAN
Refers to the results that have been rigorously proven.
CERTAINTY IN MATHEMATICS
The fundamental principles, axioms, and definitions upon which the entire mathematical edifice is built.
FOUNDATION/S
What is one of the famous paradoxes by Zeno?
Paradox of Achilles and the Tortoise
TRUE OR FALSE
Certainty in mathematics is crucial for understanding and managing errors and certainties.
FALSE
UNCERTAINTIES in mathematics is crucial for understanding and managing errors and certainties.
In what era or centuries did Isaac Newton and Gottfried Wilhelm Leibniz develop calculus?
Renaissance and Early Modern Mathematics or 15th - 18th centuries
Implies that the logical processes and deductive reasoning used in mathematical proofs are free from error.
INFALLIBILITY IN MATHEMATICS
A logical argument that demonstrates the truth of a mathematical statement beyond any reasonable doubt.
RIGOROUS PROOF/S
FILL IN THE BLANKS
Notable efforts include Bertrand Russell and Alfred North Whitehead's monumental work "_____________," which aimed to establish the logical foundations of mathematics based on set theory and formal logic.
PRINCIPIA MATHEMATICA
TRUE or FALSE
Mathematics, though a powerful tool, is immune to biases and inequalities present in society.
FALSE
Mathematics, though a powerful tool, is NOT immune to biases and inequalities present in society.
They developed sophisticated techniques for calculation and problem-solving.
The Mesopotamians, particularly the Sumerians and Babylonians.
Identify which of Godel’s incompleteness theorems refers to this statement.
"Extends the first one by stating that such a formal system cannot prove its own consistency. "
SECOND Incompleteness Theorem
TRUE OR FALSE
Logicism theory emphasizes the constructive nature of mathematics.
FALSE
It is not the logicism theory; rather, it is the intuitionism theory.
IDENTIFY WHAT THE CONTROVERSY IS BASED ON THE STATEMENT.
"Philosophical debates surrounding the nature of mathematical objects and the foundations of mathematics have long been contentious."
Intuitionism vs. Formalism vs. Platonism
TRUE or FALSE
Certainty in mathematics contributes to the robustness and resilience of technologies.
TRUE
TRUE OR FALSE
The Euclidean developed the geometries that challenged traditional notions of space and geometry?
FALSE
It was not the Euclidean rather they are non-Euclidean that developed the geometries that challenged traditional notions of space and geometry.
Enumerate the key concepts of Godel’s Incompleteness Theorems.
Consistency, Completeness and Formal System.
This approach ensures that mathematical results are reliable and free from error.
RIGOROUS APPROACH
This theory deals with the unpredictability of deterministic systems, posing challenges to traditional notions of predictability and determinism in mathematics.
CHAOS THEORY
Which of the following is the Role of Certainty in Mathematics for Applied Fields and Technology
a. Error Analysis and Tolerance
b. Communication and Transparency
c. Ethical Considerations
d. Interdisciplinary Collaboration
a. Error Analysis and Tolerance
In what era or century did mathematicians challenge their understanding of numbers with irrational numbers?
Ancient Greece or circa 600 BCE - 300 CE
Name the following three reasons for the value of infallibility and certainty in mathematics.
1st Statement:
"Mathematical certainty ensures that solutions to problems are correct and reliable."
2nd Statement:
"The quest for certainty has driven the evolution of mathematical theories and methodologies."
3rd Statement:
"Mathematical truths are consistent and universal, meaning they hold true across different contexts and cultures."
Reliability in Problem Solving, Progress in Mathematical Theories and Consistency and Universality.
Enumerate the several reasons why the importance of rigorous proof cannot be overstated.
Ensuring Accuracy
Establishing Truth
Building on Foundations
Fostering Confidence
Identify the paradox based on the statement.
"This paradox raises questions about the nature of language, logic, and self-reference."
Grelling–Nelson Paradox
The following are the Societal Implications of Relying on Mathematics as a Source of Certainty except;
a. Trust and Authority
b. Interdisciplinary Collaboration
c. Rigorous Mathematical Foundations
d. Communication and Transparency
c. Rigorous Mathematical Foundations
In this era their mathematics lack rigorous proof. Mistakes and inaccuracies were common, but they laid the groundwork for future mathematical developments.
Mesopotamia