What Does Numbers Mean? Symbols Explained

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Discussion Overview

The discussion revolves around the nature and meaning of numbers and mathematical symbols. Participants explore the conceptual foundations of numbers, their interpretations, and the significance of symbols in mathematics.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that numbers do not have inherent meanings and are defined by the interpretations we assign to them, such as representing quantities.
  • Others argue that symbols in mathematics, like numbers, are agreed-upon representations that can vary in meaning based on context.
  • A participant suggests that numbers serve as adjectives that provide information about quantities related to nouns.
  • Another viewpoint emphasizes that numbers alone lack meaning until they are ordered or contextualized.
  • Some contributions highlight that context is essential for understanding the meaning of both words and numbers.
  • A participant presents an example of how numbers can represent complex information, such as digital images or audio files, suggesting a broader application of numbers beyond simple quantities.
  • There is a reiteration that the meaning of specific numbers, like "one," is akin to the meaning of names, implying that they are arbitrary without context.

Areas of Agreement / Disagreement

Participants generally agree that numbers and symbols require context for meaning, but there are multiple competing views on whether numbers have inherent meanings or if they are purely contextual constructs. The discussion remains unresolved regarding the nature of numbers and their interpretations.

Contextual Notes

Some assumptions about the definitions of numbers and symbols are not explicitly stated, leading to varying interpretations of their meanings. The discussion does not resolve the complexities of how numbers relate to physical concepts or abstract ideas.

hanilk2006
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What are numbers??

Hello there intellectuals!

What are numbers? what does it represent? because isn't math basically bunch of symbolism that everybody agreed upon?

so Please tell me what numbers mean!

and also what are these symbols mean?: +, -, x, /
 
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That's the wonderful part: numbers are just numbers! They don't have any interpretation attached to them, which frees us to use them for a wide variety of tasks.

What a number represents is defined by the interpretation. For example, we could interpret numbers as representing some intuitive notion of "quantity". Experience has shown the natural numbers interpreted this way are a rather good way to capture that intuitive notion, and so we use it.

This works the other way too -- if we do not yet have intuition about natural numbers, we can assist our intuition by interpreting them as a hypothetical quantity. (even if we are using natural numbers in a way that has nothing to do with quantity!)
 


i thought symbols had one meaning attached to it though. Don't people decide what concept the symbol is going to represent? For instance the bathroom door sign? the one without the skirt is men?
 


Numbers are adjectives; they give information about quantity for the modified noun. In practice, numbers express the count or the measure of something. As something worth studying, numbers are ideas, which may then be nouns.
 


hanilk2006 said:
Hello there intellectuals!

What are numbers? what does it represent? because isn't math basically bunch of symbolism that everybody agreed upon?

so Please tell me what numbers mean!

and also what are these symbols mean?: +, -, x, /

Like Hurkyl mentioned, numbers are numbers.

Numbers represent some kind of information.

Think about say a picture. Let's say its 100x100 pixels with 256 shades of red, 256 shades of blue and 256 shades of green. You could represent this picture with a number that has
log_2(256*256*256)^(100x100) = 10,000 log(2^24) = 240,000 log_2(2) = 240,000 bits which is 30,000 bytes. So basically you could represent any picture 100x100 with 256 shades of red,blue and green with a number ranging from 0 to 2^(240,000) - 1.

Your audio file (raw output) can be represented with a single number in the same kind of way.

Typically though scientists usually deal with things that are physical like distance, time, temperature and so on. But like the examples above you can represent anything with a single number if you want, you just have to have some unique way to turn your number into the kind of object that the number actually represents.
 


The question what does "one" mean is the same as what does" John" mean, nothing.
Numbers by themselves mean nothing, it is only when you give them order are they meaningful.
 


Words (or numbers) on their own mean nothing. Always.
Context is what gives words meaning.
 


coolul007 said:
The question what does "one" mean is the same as what does" John" mean, nothing.
Numbers by themselves mean nothing, it is only when you give them order are they meaningful.

Two means two groupings of traits, it is something in the mind. The universe understands one, none, and infinity.
 

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