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anemone
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Let $x$ be a real number such that $x=(x-1)^3$. Show that there exists an integer $N$ such that $-2^{1000}<x^{2021}-N<2^{-1000}$.
anemone said:Let $x$ be a real number such that $x=(x-1)^3$. Show that there exists an integer $N$ such that $-2^{{\color{red}-}1000}<x^{2021}-N<2^{-1000}$.
An integer is a whole number, either positive or negative, without any fractions or decimals. Examples of integers include -3, 0, and 7.
To solve an integer and inequality, you need to isolate the variable on one side of the inequality symbol. Then, you can use inverse operations to solve for the variable. If the inequality symbol is less than or greater than, the solution will be an open interval. If the inequality symbol is less than or equal to or greater than or equal to, the solution will be a closed interval.
This notation means that the value of x is equal to the quantity of x-1 raised to the power of 3. In other words, the value of x is equal to the cube of x-1.
An integer is a specific type of number, while an inequality is a mathematical statement that compares two values. An integer can be used in an inequality, but an inequality cannot be used in place of an integer.
The solution for x=(x-1)^3 for N is N=1. This can be found by substituting N for x in the original equation and solving for N.