3pointonefour
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If you want to compare 2 numbers, but you're unsure of which is bigger than the other (or if they're the same), is there a particular symbol for that? Like if we were to write "a is either greater than, less than or equal to b" is there a way of writing that with a single symbol instead of (a ≥ b U a < b)? Thanks in advance
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vicvic38
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I'm curious as to why you need this symbol.

The reals have the property of Trichotomy, meaning for all elements a,b in the reals, one of the following is true:

a<b, a = b or a>b.

There isn't a symbol past the usual both are in the reals.
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loganau2001
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By saying "a is either greater than, less than or equal to b", that basically means that 'a' can be any number since the statement says that it could be equal to 'b' or not equal to 'b'.

So no, there is no single symbol that could describe the statement you wrote. Hope that helps
(Original post by 3pointonefour)
If you want to compare 2 numbers, but you're unsure of which is bigger than the other (or if they're the same), is there a particular symbol for that? Like if we were to write "a is either greater than, less than or equal to b" is there a way of writing that with a single symbol instead of (a ≥ b U a < b)? Thanks in advance
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Meowstic
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a,b ∈ ℝ
i guess
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RDKGames
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(Original post by 3pointonefour)
If you want to compare 2 numbers, but you're unsure of which is bigger than the other (or if they're the same), is there a particular symbol for that? Like if we were to write "a is either greater than, less than or equal to b" is there a way of writing that with a single symbol instead of (a ≥ b U a < b)? Thanks in advance
No, there is no such symbol.

If you want the bigger of the two, you denote this as \max \{ a,b\}.

If you want the lesser of the two, you denote this as \min \{ a,b \}.
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3pointonefour
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(Original post by RDKGames)
No, there is no such symbol.

If you want the bigger of the two, you denote this as \max \{ a,b\}.

If you want the lesser of the two, you denote this as \min \{ a,b \}.
Much appreciated
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3pointonefour
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(Original post by vicvic38)
I'm curious as to why you need this symbol.

The reals have the property of Trichotomy, meaning for all elements a,b in the reals, one of the following is true:

a<b, a = b or a>b.

There isn't a symbol past the usual both are in the reals.
The question was "which is bigger, 999^1000 or 1000^999?"
So I wanted to use this symbol to write 999^1000 (insert symbol here) 1000^999 ==> 999^(1/999) (insert symbol here) 1000^(1/1000).
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Alpacamatrix
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(Original post by 3pointonefour)
The question was "which is bigger, 999^1000 or 1000^999?"
So I wanted to use this symbol to write 999^1000 (insert symbol here) 1000^999 ==> 999^(1/999) (insert symbol here) 1000^(1/1000).
Is it the first one? generally a power has a bigger effect that the base
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mqb2766
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Generally an operator constrains the set of "solutions", what you're asking for here doesn't so there isn't really a role for such an operator.

In this case, I suspect you're not gping diwn the right path. A couple of ways of doing it.
1) Quick and dirty, use logs and a calculator.
2) Use a binomial expansion of 1000^999 and show its less than e*999^999.


(Original post by 3pointonefour)
The question was "which is bigger, 999^1000 or 1000^999?"
So I wanted to use this symbol to write 999^1000 (insert symbol here) 1000^999 ==> 999^(1/999) (insert symbol here) 1000^(1/1000).
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3pointonefour
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#10
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(Original post by mqb2766)
Generally an operator constrains the set of "solutions", what you're asking for here doesn't so there isn't really a role for such an operator.

In this case, I suspect you're not gping diwn the right path. A couple of ways of doing it.
1) Quick and dirty, use logs and a calculator.
2) Use a binomial expansion of 1000^999 and show its less than e*999^999.
I just graphed and found the maximum point of y = x^(1/x) and saw it's a decreasing function when x ≥ e
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3pointonefour
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#11
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(Original post by Alpacamatrix)
Is it the first one? generally a power has a bigger effect that the base
999^1000 > 1000^999, so yep you're right
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