Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Non-uniqueness of hyperreal extensions means infinitely m... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→Regularity can be preserved for uncountable sample spaces by using hyperreal-valued probability functions

    Non-uniqueness of hyperreal extensions means infinitely many incompatible regular hyperreal probability functions exist for the same sample space, making regularity indeterminate rather than preserved.

    ?Rate how convincing each reason is below to see the overall strength.

    No one has weighed in yet. Be the first to share reasons for or against this statement.

    Sign in or register to share your perspective on this statement.

    Key Terms

    Hyperreal extensions(in probability theory and mathematical logic)
    A mathematical system that extends regular numbers to include infinitesimally small and infinitely large quantities, used to make certain mathematical problems easier to solve.
    Indeterminate(Reichenbach's three-valued quantum logic)
    The value of propositions that quantum theory implies cannot be assessed to be either true or false
    Non-uniqueness(in mathematics and logic)
    The quality of having more than one possible answer or version instead of just one correct answer.
    Probability functions(describes what the inductive logic uses to measure likelihood)
    Mathematical tools that calculate how likely something is to be true, assigning numbers between 0 (impossible) and 1 (certain) to different outcomes.

    Next step

    Based on where you are in your exploration

    Explore a random proposition
    Start fresh with something unrelated.
    Regularity (in probability)(in formal probability theory)
    A property where every possible outcome in a probability system has some non-zero chance of occurring—nothing is completely impossible.
    Sample space(a mathematical concept needed to make fair comparisons)
    In probability and statistics, the complete set of all possible outcomes you're considering; for example, the sample space for a coin flip is 'heads' or 'tails'.
    incompatible(as used to describe conflicting demands or responsibilities)
    Unable to exist or work together at the same time; conflicting with each other.

    Connections

    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Regularity can be preserved for uncountable sample spaces by using hyperreal-val...

    Details

    Type
    claim
    Perspectives
    0 (0 for, 0 against)
    Edits
    1 edit

    Open for perspectives

    This idea is waiting for its first supporting or challenging perspective.

    Share the first perspective