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# How does it work ?

spinout
If you take away the smallest number ever from 1, what have you then in this universe?
kelseymh
 spinout wrote: If you take away the smallest number ever from 1, what have you then in this universe? I am not sure I understand the meaning with the question above, please help me!

What do you think you mean by your question? As written, it doesn't make any sense.
Smallest number ever, is there such a number? If there is no such number the answer to you question must be "nothing".
If you talk about natural numbers the smallest number would be 0 or 1 so the answer would be 1 or 0 depending on what definition of natural numbers you use.

EDIT: Or maybe it's a trick question. If we just focus on this part of the question "what have you then in this universe?". I guess everything in the universe is still there so then you have everything that you had before. The question is very ambiguous!
_AVG_
If you are referring to a 'smallest number' in magnitude, there is no such number. The proof is pretty simple. Let x > 0 be the smallest positive number. Then x/2 < x so x cannot be the smallest number. If you're talking about a 'smallest integer', that doesn't exist either. Let x be the smallest integer. Then x-1<x so x cannot be the smallest integer. So the negative numbers also stretch all the way down to negative infinity, which is undefined to our finite minds. This is similar to the proof of the nonexistence of any 'largest number'. If x is the largest number, x+1>x so x cannot be the largest number.
Of course, you can have a largest and/or smallest number if you discard the laws of logic
ocalhoun
 _AVG_ wrote: If you are referring to a 'smallest number' in magnitude, [...]. If you're talking about a 'smallest integer', that doesn't exist either.

Well, in magnitude terms, there is a smallest integer, 0.
All other integers have a greater magnitude than that one.

As for the original question:
 Quote: If you take away the smallest number ever from 1, what have you then in this universe?

As AVG noted, it makes no sense to think of 'the smallest number ever' in terms of 'the largest magnitude negative number ever', because there is no limit.
So, I'll assume it means taking away the smallest (magnitude) number ever... Which would be 0.
And in this universe, when you subtract 0 from 1, you get 1.
...I'd even go as far as to say basic mathematics like that should work the same in every universe.
(I'd hate to try to learn the mathematics of a universe where 1-0=/=1, that's for sure!)

Well, that's my best understanding of the question.
Dennise
 spinout wrote: If you take away the smallest number ever from 1, what have you then in this universe? I am not sure I understand the meaning with the question above, please help me!

Mathematically, as others have stated, you are left with a number that is arbitrarily less than 1. But for any number you may think is the 'smallest' number ... say X, there is still a smaller number X/2. I.e. you will never reach the 'smallest number' but instead will get arbitrarily closer to zero as you search in vain for the smallest number. This is one of the tenants of calculus.

By 'in this universe', I assume you are referring to mathematics as we know it in our known universe.
nguyenvulong
Who ask you such a question
or do you have some sources ?

It sounds non-sense .
orangbaik
 spinout wrote: If you take away the smallest number ever from 1, what have you then in this universe? I am not sure I understand the meaning with the question above, please help me!

you will have the number of limit 1 or in other word none
asnani04
If the question is valid, we'd still have all the things in the universe that are present right now, isn't it?
LxGoodies
 spinout wrote: If you take away the smallest number ever from 1, what have you then in this universe?

I would say exactly the same universe. Nothing will change. Mass, energy and matter all get preserved, so it's impossible to remove anything away from the universe. Everything will stay inside, forever.

Lx
sathishbl
 spinout wrote: If you take away the smallest number ever from 1, what have you then in this universe? I am not sure I understand the meaning with the question above, please help me!

i think the answer is 0, because according to scale wise zero is the smallest digit....so its meaning is that when you remove the smallest number from 1 it will be zero in this universe.
playfungames
If only there was a way to find out the smallest number. I mean, 0.<million zeroes>1 is still not the smallest numbers. It so confusing and I guess that is how the universe is...CONFUSING!!
Bikerman
Clearly there is no single smallest number because, just as with the 'largest' number, one can always subtract one (or a fractional part) to give a smaller number.
The set of integer numbers is infinite in 'both directions' - ie the set tends to infinity in both the positive and negative 'directions' along the number line.
Clearly 0 cannot be the smallest number, unless one defines 'smallest' in a way which is not currently the accepted definition. -1 MUST be smaller than 0 and, by the same argument, -2 is smaller than -1.

The argument about 'removing the smallest number from 1' to leave 0 is both confused and rather silly.
SonLight
 spinout wrote: If you take away the smallest number ever from 1, what have you then in this universe? I am not sure I understand the meaning with the question above, please help me!

Nor can any of us understand "the" meaning, since there are serious ambiguities in it.

As others have mentioned, one interpretation is that the process of subtraction doesn't affect "this universe" a whole lot, so one plausible answer is "the same universe".

Another meaning for "in this universe" is that the rules of math and physics are as we know them, not as they might be or theoretically could be in some alternative universe, inside a black hole, or some stranger place if you can think of it. I can't think of a possible 'universe' where mathematical principles would be radically different, but I couldn't have ruled it out except that the question suggests I shouldn't try warp drive or strange geometries to see if the result changes.

Yet another meaning of "universe" is a specified "universal set". That would specify the context and perhaps the types of numbers allowed. Usually mathematicians are careful to use more precise terms, such as "in the universe of natural numbers", "in the universe of integers", etc.

If we do interpret the question "in the universe of natural numbers", then only the positive integers qualify and zero does not. In that case, and only in that case, the result of the subtraction is not in the set of natural numbers. While the answer is undefined, that is potentially the most useful result as it might encourage us to define a larger universal set.
LxGoodies
 Sonlight wrote: only the positive integers qualify and zero does not

With natural numbers the answer is straightforward 1-1=0 (one is the smallest number )

Lx
Bikerman
Nope. First you have to say whether the 'natural' numbers include 0 or not - there are two schools of thought on that. If you DO include 0 (and YOU do, because you used 0 in your example above) then 0n is the smallest number in your system of representation. If you DON'T include 0 in the 'natural' or 'counting' numbers then you also have to rule out all non-integer quantities such as 1/2 1/3 etc which allows you to have 1 as your smallest number, but gives you a bloody useless system of representation for most real-life purposes, other than counting simply integer quantities. Fine for small sheep/cattle farmers with a few beasts, but not much use for anything else.
This is, in a roundabout way, why the Romans never progressed to the heights one might have expected in engineering - their numeral system was really crappy system for doing useful arithmetic, let alone proper maths.....
LxGoodies
 Bikerman wrote: but gives you a bloody useless system of representation for most real-life purposes

Hmm I would not dare to say N+ (which is the collection I referred to) is of any practical use , but the smallest number in N+ is 1. And 1-1=0, yielding an outcome which is not in N+. But this also counts for subtracting something from 0 which would yield a minus value, outside the collection. If you require that both operand and outcome are in the same collection, the most logical approach would be to interpret both as R-members, yielding

1 - 1/INF = 0.999999999999999999999999999999999999999999999999999999999 (etc)

.. with 1/INF (one divided by infinity) as "smallest number".

Lx
nguyenvulong
There're many "types" of number, real unreal (complex number) decimal, hexa decimal
so it's no doubt that you can have a smaller number .