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sql - mysql update a column with an int based on order

Lets say I have these columns

 uniqueID|Money|Quantity|MoneyOrder|QuantityOrder
1|23|12||
2|11|9||
3|99|100||

What I want to do is update MoneyOrder and QuantityOrder based on the value of ORDER BY.

So the results would be:

uniqueID|Money|Quantity|MoneyOrder|QuantityOrder
1|23|12|2|1
2|11|90|1|2
3|99|100|3|3

I want the update to operate like an identity column without actually making it an identity column. I know that I could just order by 'x' and the order would be the result but I want to generate a report where you can see the item line by line.

Is something like this possible update mytable set Moneyorder = 'imnotsure' order by MoneyOrder asc ?

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SET @rownumber = 0;    
update mytable set Moneyorder = (@rownumber:=@rownumber+1)
order by MoneyOrder asc

or to do it in a single query you can try

update mytable target
join
(
     select id, (@rownumber := @rownumber + 1) as rownum
     from mytable         
     cross join (select @rownumber := 0) r
     order by MoneyOrder asc
) source on target.id = source.id    
set Moneyorder = rownum

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