Nothing & infinity

[GregoryC]

Summary:: Would nothing & infinity be considered polar opposites? Neither can be observed and are hypothetical at 2 extremes.

"Nothing" is one of the questions much like "infinity", I find myself questioning these supposedly two "real" expressions. Logically they both make sense.

 

[phinds]

I think you are trying to say that apples are the opposite of oranges. They're just different things. Even zero and infinity are not opposites since zero is a number and infinity is something else entirely.

 

[jbriggs444]

Both zero and infinity are absent from the multiplicative group within the real numbers.

 

[kuruman]

With a generous amount of tongue in cheek, I would say that minus infinity is the polar opposite of infinity with nothing in the middle. After all, when you add infinity and minus infinity, you get nothing.

 

[Nugatory]

Any time that you find yourself trying to do math with infinity or the reciprocal of zero, or any physical system in which some measurable quantity is exactly equal to zero... STOP. You're about to make a mistake. Restate your problem in terms of limits, and then do the calculation.

 

[256bits]

And infinitesimals are the opposite of ... ?

 

[PeroK]

Summary:: Would nothing & infinity be considered polar opposites? Neither can be observed and are hypothetical at 2 extremes.

"Nothing" is one of the questions much like "infinity", I find myself questioning these supposedly two "real" expressions. Logically they both make sense.

You can have a zero balance on your bank account. So, IMO, zero is a fairly simple concept. Mathematically speaking, the opposite of a large (in credit) bank balance is a large negative bank balance. Although, in everyday language you could say that the opposite of having a lot of money is to have none.

Mathematically, "infinity" appears in a number of contexts. There is the concept of an infinite set, for example. This means a set that is "not finite", like the whole numbers: $\{0, 1, 2, 3 \dots \}$. If this set were finite, then there must be a largest possible whole number. But, you can always add $+1$ to any whole number to get another one. The set of whole numbers, therefore, is not finite, and we call it an infinite set.

 

[GregoryC]

I thank you for the answers, although I am not referring to 0, I am referring to "nothing", which is a different concept than 0.

 

[PeroK]

I thank you for the answers, although I am not referring to 0, I am referring to "nothing", which is a different concept than 0.

Nothing is represented in mathematics by the empty set.

 

[jbriggs444]

Nothing is represented in mathematics by the empty set.

Zero in mathematics is also sometimes represented by the empty set.

 

[mjc123]

Zero in mathematics is also sometimes represented by the empty set.

Therefore the empty set represents something, so it is not true that the empty set represents nothing!

Reminds me of the old joke: The pain-killer Anadin used to be advertised with the slogan "Nothing acts faster than Anadin". The joke went: What's the best thing to take for a headache? Answer: nothing, because nothing acts faster than Anadin.

Seriously, this warns us of the slippery use of language, especially in common parlance without clear definitions. As someone said recently in another thread: if you want to be clear and unambiguous, use math, not language. It is a classic fallacy to assume that if there is a word, there must be an entity corresponding to that word, about which we make statements when we use the word, e.g if we say "nothing moves faster than light", we are postulating an entity called Nothing that moves faster than light (or acts faster than Anadin). This is parodied by Lewis Carroll in "Through the Looking-glass" (‘Who did you pass on the road?’ the King went on, holding out his hand to the Messenger for some more hay. ‘Nobody,’ said the Messenger. ‘Quite right,’ said the King: ‘this young lady saw him too. So of course Nobody walks slower than you.’ ‘I do my best,’ the Messenger said in a sulky tone. ‘I’m sure nobody walks much faster than I do!’ ‘He can’t do that,’ said the King, ‘or else he’d have been here first.')

"Opposite" is also a slippery concept in ordinary language. It's often used to describe things that are often paired and contrasted, e.g. male/female or cat/dog, that are not logical opposites. The bank account illustration in post #7 is another instance.

 

[pinball1970]

I thank you for the answers, although I am not referring to 0, I am referring to "nothing", which is a different concept than 0.

You have to define what you mean by nothing otherwise you end up on the road to philosophy.edit: Instead of the road to reality i can't believe I missed that opportunity.

Two book refs? Easy (ish) reads? One two three infinity Gamow and A universe from nothing Krauss