Is Oxyhydrogen a spontaneous reaction at very high temperatures?

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ineedaquickie
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Hi, this may seem like a noob question for you geeks out there, but I can't wrap my head around this.
The formula for a spontaneous reaction is [itex]\Delta[/itex]H-T[itex]\Delta[/itex]S < 0
Basically, since the reaction between hydrogen and oxygen gas has a negative change in enthalpy it must mean that if the temperature in Kelvin is big enough then the reaction between oxygen and hydrogen gas will not be spontaneous.

Because the negative T multiplied with the negative change in entropy will be more positive than the enthalpy change and it won't be a spontaneous process? right?
 
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I'm sorry to bring this up, but does the same count for the burning of magnesium. Burning of magnesium is exothermic, but the change in entropy is negative as well so if the temp is big enough, the reaction won't be spontaneous. Correct?