Introduction:
The liberal notion of equality is based on the principles of individual rights, freedom, and equal opportunity. It upholds the idea that all individuals should be treated equally under the law and have the same political rights and opportunities. However, there are different types of equality that can be considered incompatible with the liberal notion of equality. Among these, economic equality is the one that stands out as not compatible.

Explanation:
- Legal equality: Legal equality refers to the principle that all individuals should be treated equally under the law. This means that everyone is entitled to the same legal rights and protections, regardless of their race, gender, or social status. Legal equality is compatible with the liberal notion of equality as it ensures that all individuals have equal access to justice and are protected by the same laws.

- Political equality: Political equality means that all individuals have equal opportunities to participate in the political process and have their voices heard. It ensures that everyone has the right to vote, stand for office, and express their opinions freely. Political equality is also compatible with the liberal notion of equality as it guarantees that all individuals have an equal say in shaping the policies and decisions that affect their lives.

- Social equality: Social equality refers to the idea that all individuals should have equal access to social resources, opportunities, and benefits. It aims to eliminate social hierarchies and inequalities based on factors such as wealth, education, or social status. While social equality is an important aspect of social justice, it can be seen as somewhat incompatible with the liberal notion of equality. Liberalism emphasizes equal opportunity rather than equal outcomes, and therefore, it does not advocate for complete social equality.

- Economic equality: Economic equality entails the equal distribution of wealth, income, and resources among individuals. It seeks to eliminate disparities in economic status and ensure that everyone has access to the same economic opportunities and benefits. However, economic equality is not compatible with the liberal notion of equality. Liberalism values individual freedom and acknowledges the importance of private property rights and free markets. It does not advocate for government-mandated redistribution of wealth or income. Instead, liberalism promotes equal opportunity in the economic sphere, allowing individuals to pursue their own economic goals and ambitions.

Conclusion:
While legal equality, political equality, and to some extent, social equality are compatible with the liberal notion of equality, economic equality is not. Liberalism prioritizes individual freedom and equal opportunity over equal outcomes in the economic sphere. It supports free markets and private property rights rather than advocating for government intervention to achieve economic equality.