Let's break down the two statements one by one:

1. For all $x$ in real numbers, there exists a $y$ in real numbers such that $x < y$:

   This statement is True. For any real number $x$, you can always find another real number $y$ that is greater than $x$. For example, if $x = 100$, you can choose $y = 101$ or $y = 1000$, etc. Since the real numbers are unbounded above, there is always a $y$ such that $x < y$.

2. There exists an $x$ in real numbers such that for all $y$ in real numbers, $x < y$:

   This statement is False. There is no real number $x$ that is less than all other real numbers because the real numbers are unbounded below. For any $x$, you can always find a smaller $y$. Therefore, no single $x$ can satisfy the condition of being less than all $y$.

Summary:

1. True.
2. False.

Would you like further explanation or details?

Here are some related questions:

1. What is the difference between bounded and unbounded sets?
2. Can you explain the concept of real numbers being unbounded?
3. Is there a largest or smallest real number?
4. What happens in similar conditions for rational or irrational numbers?
5. How does the concept of infinity relate to real numbers?

Tip: Understanding how real numbers are unbounded both above and below is essential in many mathematical fields, especially calculus and analysis.